Stochastic Finance @ Warwick Seminars
Unless otherwise stated, the seminars will take place on Wednesdays at 11:00 am, in B3.03 (Zeeman). Please contact Nazem Khan or Gechun Liang for further details.
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Postponed |
Jae Hyoung Kim (University of Oxford) Title: Network Finance: The Life Cycle of Issuer Dependence Abstract: Exploiting data on token-financed networks and information technology shocks, this paper shows that issuer information is positively associated with network adoption, but the association weakens as networks mature. The decline in issuer dependence is concentrated in ongoing rather than initial issuer information, while external information production through community engagement is associated with network adoption over longer horizons. The life-cycle pattern is robust and is not easily attributable to changes in network development. Evidence from token returns further sheds light on the increasing economic importance of network activity relative to continued issuer efforts. |
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| TBC | Edward Wang (Hong Kong) | ||||||||
| 4th November | Jos茅 Pedraza Ram铆rez (University of Manchester) Title: Optimal Stopping for Exponential L茅vy Models with Weighted Discounting Abstract: In this talk, we consider an optimal stopping problem with weighted discounting, and the state process is modelled by a general exponential L茅vy process. Due to the time inconsistency, we provide a new martingale method based on a verification theorem for the equilibrium stopping strategies. As an application, we generalise an investment problem with non-exponential discounting studied by Grenadier and Wang (2007) and Ebert et al. (2020) to L茅vy models. Closed-form equilibrium stopping strategies are derived, which are closely related to the running maximum of the state process. The impacts of discounting preferences on the equilibrium stopping strategies are examined analytically. |
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| 18th November | Meet the MF Group: short talks by PhD students. All welcome; especially CDT students and Masters students. |
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| 2nd December | Kay Giesecke (Stanford University) | ||||||||
Unless otherwise stated, the seminars will take place on Wednesdays at 11:00 am, in B3.03 (Zeeman). Please contact Nazem Khan or Gechun Liang for further details.
| 20th January | Moris Strub (天美传媒) |
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| 27th January | Philipp Plank (Imperial College London) | ||||||||
Unless otherwise stated, the seminars will take place on Wednesdays at 11:00 am, in B3.03 (Zeeman). Please contact Nazem Khan or Gechun Liang for further details.
Unless otherwise stated, the seminars will take place on Wednesdays at 11:00 am, in B3.03 (Zeeman).
| 15th October | Pavel Gapeev (LSE)
Title: Perpetual American Standard and Lookback Options in Models with Progressively Enlarged Filtrations
Abstract:
We derive closed-form solutions to optimal stopping problems related to the pricing of perpetual American standard and lookback put and call options in extensions of the Black-Merton-Scholes model under progressively enlarged filtrations. It is assumed that the information available from the market is modelled by Brownian filtrations progressively enlarged with the random times at which the underlying process attains its global maximum or minimum, that is, the last hitting times for the underlying risky asset price of its running maximum or minimum over the infinite time interval, which are supposed to be progressively observed by the holders of the contracts. We show that the optimal exercise times are the first times at which the asset price process reaches certain lower or upper stochastic boundaries depending on the current values of its running maximum or minimum depending on the occurrence of the random times of the global maximum or minimum of the risky asset price process. The proof is based on the reduction of the original necessarily three-dimensional optimal stopping problems to the associated free-boundary problems and their solutions by means of the smooth-fit and either normal-reflection or normal-entrance conditions for the value functions at the optimal exercise boundaries and the edges of the state spaces of the processes, respectively.
This is joint work with Libo Li (Sydney).
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| 12th November | Meet the MF Group: short talks by PhD students. All welcome especially CDT students and Masters students. Jing Liu Title: Optimal Stopping of a Brownian Excursion and an $\alpha-$dimensional Bessel Bridge
Florian Gutekunst Title: Optimal Investment and Consumption in a Stochastic Factor Model Edward Wang Title: Nonzero-sum Dynkin games under a generalised order condition |
| 13th November (11:00 am, B3.03) | Xin Guo (UC Berkeley) Title: From LLM to RL and diffusion models, via (rough) differential equations Abstract: Transfer learning is a machine learning technique that leverages knowledge acquired in one domain to enhance performance on a related task. It plays a central role in the success of large language models (LLMs) such as GPT and BERT, which leverage pretraining to enable broad generalization across downstream applications. In this talk, I will discuss how reinforcement learning (RL), and in particular continuous time RL, can benefit from transfer learning principles. I will present convergence results formulated through stability analysis for stochastic control systems, using rough differential equation techniques. Finally, I will show how this analysis yields a natural corollary establishing robustness guarantees for a class of score-based generative diffusion models. Based on joint work with Zijiu Lyu of UC Berkeley. |
| 3rd December | Xinyu Li (Oxford) Title: An alpha-potential game framework for N-player potential games Abstract:
We propose and study a general form of dynamic N-player non-cooperative games called alpha-potential games, where the change of a player's objective function upon her unilateral deviation from her strategy is equal to the change of an alpha-potential function up to an error alpha. Analogous to the static potential game (which corresponds to alpha=0), the alpha-potential game framework is shown to reduce the challenging task of finding alpha-Nash equilibria for a dynamic game to minimizing the alpha-potential function. Moreover, an analytical characterization of alpha-potential functions is established, with alpha represented in terms of the magnitude of the asymmetry of objective functions' second-order derivatives. For stochastic differential games in which the state dynamic is a controlled diffusion, alpha is characterized in terms of the number of players, the choice of admissible strategies, and the intensity of interactions and the level of heterogeneity among players. To analyze the alpha-NE, the associated optimization problem is embedded into a conditional McKean鈥揤lasov control problem. A verification theorem is established to construct alpha-NE based on solutions to an infinite-dimensional Hamilton-Jacobi-Bellman equation, which is reduced to a system of ordinary differential equations for linear-quadratic games.
We also analyze a broad class of distributed games with jump diffusions using the alpha-potential gameframework. We demonstrate that analyzing the alpha-Nash equilibria reduces to solving a finite-dimensional control problem. Beyond the viscosity and verification characterizations for the general games, we explicitly and in detail examine how spatial population distributions and interaction rules influence the structure of alpha-Nash equilibria in these distributed settings, and in particular for crowd motion games. Our theoretical results are supported by numerical implementations using policy gradient-based algorithms, further demonstrating the computational advantages of the alpha-potential game framework in computing Nash equilibria for general dynamic games.
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| 10th December | Jonathan Tam (Oxford) Title: Bayesian dynamic portfolio optimization with informative constraints Abstract:
There is a recent debate on whether sustainable investing necesarily impact portfolio performance negatively. We model the financial impact of portfolio constraints by attributing the performance of dynamic portfolios to contributions from individual constraints. We consider a mean-variance portfolio problem with unknown asset returns. Investors impose a dynamic constraint based on a firm characteristic that contains information about returns, such as the environmental, social, and governance (ESG) score. We characterize the optimal investment strategy through two stochastic Riccati equations. Using this framework, we demonstrate that, depending on the correlation between returns and firm characteristics, incorporating the constraint can, in certain cases, enhance portfolio performance compared to a passive benchmark that disregards the information embedded in these constraints. Our results shed light on the role of implicit information contained in constraints in determining the performance of a constrained portfolio.
This project is joint work with Ruixun Zhang (Peking University), Yufei Zhang (Imperial College London) and Xunyu Zhou (Columbia University).
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Unless otherwise stated, the seminars will take place on Wednesdays at 11:00 am in B3.03 (Zeeman). Please contact Gechun Liang for further details.
| 21 January | Philipp Jettkant (Imperial College) Title: A Forward-Backward Approach to Endogenous Distress Contagion
Abstract: In this talk, I will introduce a dynamic model of distress contagion in banking networks. Distress is propagated in the system through credit value adjustments that banks apply to interbank obligations to reflect counterparty default risk, causing excess volatility. The counterparty default risk is computed backward in time from the obligations' maturity date, leading to a specification of the model as a singular forward-backward SDE coupled through the banks' default times. We analyse this equation through the associated parabolic PDE which is a novel type of tiered moving boundary problem. Each of its levels corresponds to a different configuration of solvent banks and the domain of a given level is determined by the solution of the preceding one. We establish classical well-posedness of this moving boundary problem, and then use its solution to solve the original forward-backward system and prove its uniqueness.
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| 29 January (Thursday) MB2.22 |
Yuchao Dong (Tongji University)
Title: A Two-fold Randomization Framework for Impulse Control Problems
Abstract: We propose and analyze a randomization scheme for a general class of impulse control problems. The solution to this randomized problem is characterized as the fixed point of a compound operator which consists of a regularized nonlocal operator and a regularized stopping operator. This approach allows us to derive a semi-linear Hamilton-Jacobi-Bellman (HJB) equation. Through an equivalent randomization scheme with a Poisson compound measure, we establish a verification theorem that implies the uniqueness of the solution. Via an iterative approach, we prove the existence of the solution. The existence--and--uniqueness result ensures the randomized problem is well-defined. We then demonstrate that our randomized impulse control problem converges to its classical counterpart as the randomization parameter \(\blambda\) vanishes. This convergence, combined with the value function's \(\mathcal{C}^{2,\alpha}_{loc}\) regularity, confirms our framework provides a robust approximation and a foundation for developing learning algorithms. Under this framework, we propose an offline reinforcement learning (RL) algorithm. Its policy improvement step is naturally derived from the iterative approach from the existence proof, which enjoys a geometric convergence rate. We numerically demonstrate the effectiveness of our algorithm using a widely-studied example. The results show that our RL algorithm can learn the randomized solution, which accurately approximates its classical counterpart. A sensitivity analysis with respect to the volatility parameter \(\sigma\) in the state process effectively demonstrates the exploration--exploitation tradeoff.
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| 18 Feburary |
Wei Wei (Heriot-Watt)
Title: Deep Penalty Methods: A Class of Deep Learning Algorithms for Solving High Dimensional Optimal Stopping Problems
Abstract: We propose a deep learning algorithm for high dimensional optimal stopping problems. Our method is inspired by the penalty method for solving free boundary PDEs. Within our approach, the penalized PDE is approximated using the Deep BSDE framework proposed by E et al. (2017), which leads us to coin the term "Deep Penalty Method (DPM)" to refer to our algorithm. We show that the error of the DPM can be bounded by the cost function and $O(\frac{1}{\lambda})+O(\lambda h) +O(\sqrt{h})$, where $h$ is the step size in time and $\lambda$ is the penalty parameter. This finding emphasizes the need for careful consideration when selecting the penalization parameter and suggests that the discretization error converges at a rate of order $\frac{1}{2}$. We validate the efficacy of the DPM through numerical tests conducted on a high-dimensional optimal stopping model in the area of American option pricing. The numerical tests confirm both the accuracy and the computational efficiency of our proposed algorithm.
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| 25 Feburary |
Martin Herdegen (Stuttgart) Abstract: We revisit the problem of portfolio selection, where an investor maximizes utility subject to a risk constraint. Our framework is very general and accommodates a wide range of utility and risk functionals, including non-concave utilities such as S-shaped utilities from prospect theory and non-convex risk measures such as Value at Risk. Our main contribution is a novel and complete characterization of well-posedness for utility-risk portfolio selection in one period that takes the interplay between the utility and the risk objectives fully into account. We show that under mild regularity conditions the minimal necessary and sufficient condition for well-posedness is given by a very simple either-or criterion: either the utility functional or the risk functional need to satisfy the axiom of sensitivity to large losses. This allows to easily describe well-posedness or ill-posedness for many utility/risk pairs, which we illustrate by a large number of examples. The talk is based on joint work with Leonardo Baggiani and Nazem Khan. |
| 12 March (Thursday) MB2.23 |
Math Finance Seminars from 12.30 - 16.00 A series of 5 short talks on a variety of topics in math finance. 12.30-13.10/13.10-13.50/13.50-14.30/14.40-15.20/15.20-16.00 Note the unusual location MB2.23. |
| 18 March |
Adrien RICHOU (Bordeaux)
Title: A probabilistic Numerical method for semi-linear elliptic Partial Differential Equations
Abstract: In this presentation, we study the numerical approximation of a class of Backward Stochastic Differential Equations (BSDEs) in an infinite horizon setting that provide a probabilistic representation for semi-linear elliptic Partial Differential Equations. In particular, we are also able to treat some ergodic BSDEs that are related to elliptic PDEs or ergodic type. In order to build our numerical scheme, we put forward a new representation of the PDE solution by using a classical probabilistic representation of the gradient. Then, based on this representation, we propose a fully implementable numerical scheme using a Picard iteration procedure, a grid space discretization and a Monte-Carlo approximation. We obtain an upper bound for the numerical error and we also provide some numerical experiments that show the efficiency of this approach for small dimensions. Some numerical experiments also show that it is possible to efficiently handle larger dimensions by replacing grid-based spatial discretization with neural networks. This presentation is based on [1] for the ergodic case and [2] for results concerning the non-ergodic framework.
[1] Richou, Adrien, & Shardul, Charu, Numerical approximation of Markovian BSDEs in infinite horizon and elliptic PDEs. Draft.
[2] Gobet, Emmanuel, & Richou, Adrien, & Szpruch, Lukasz, Numerical approximation of ergodic BSDEs using non linear Feynman-Kac formulas, Stochastic Process. Appl. 195 (2026)
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Unless otherwise stated, the seminars will take place on Wednesdays at 11:00 am in B3.03(Zeeman). Please contact Gechun Liang for further details.
| 6 May |
Caroline Hillairet (ENSAE-Paris) Title: Optimal Investment and Pension Policy in Pay-As-You-Go Systems under Forward Utility and ageing population Abstract : In this talk, I will present an optimal investment and pension policies in a Pay-As-You-Go (PAYG) system supplemented by a buffer fund used as an intergenerational risk鈥憇haring mechanism. The social planner鈥檚 preference criterion is represented by non-zero volatility forward Constant Relative Risk Aversion (CRRA) utilities, and explicitly accounts for both sustainability and adequacy constraints. I will characterized the optimal policies, and present new results on the impact of non-zero volatility on the pension policy, under a range of demographic, financial, and macroeconomic scenarios. Joint work with J. Alonso-Garcia, S. Kaakai and M. Mrad. |
| 13 May | Hanqing Jin (Oxford)
Title: Dynamic Mean-Variance Portfolio Selection with Transaction Costs
Abstract: We study dynamic mean-variance portfolio selection in the presence of transaction costs, aiming to identify time-consistent solutions within a game-theoretic framework. We find that while a mean-variance criterion can yield economically reasonable intrapersonal equilibrium strategies without transaction costs, it may produce economically less plausible strategies when transaction costs are present and the investment horizon is extended. Our results reveal that applying a game-theoretic framework to long investment horizons presents subtle challenges, and caution is warranted when applying it to long-horizon, time-inconsistent decision problems involving singular control. |
| 20 May | Mihails Zervos (LSE)
Ttile: A Dynamic Competitive Equilibrium Model of Irreversible Capacity Investment with Stochastic Demand and Heterogeneous Producers
Abstract: We formulate a continuous-time competitive equilibrium model of irreversible capacity investment in which a continuum of heterogeneous producers supplies a single non-durable good subject to exogenous stochastic demand. Each producer optimally adjusts both output and capacity over time in response to endogenous price signals, while investment decisions are irreversible. Market clearing holds continuously, with prices evolving endogenously to balance aggregate supply and demand through a constant-elasticity demand function driven by a stochastic base component. The model admits a mean-field interpretation, as each producer鈥檚 decisions both influence and are influenced by the aggregate behaviour of all others. We show that the equilibrium price process can be expressed as a nonlinear functional of the exogenous base demand, leading to a three-dimensional singular stochastic control problem for each producer. We derive an explicit solution to the associated Hamilton-Jacobi-Bellman equation, including a closed-form characterisation of the free-boundary surface separating investment and waiting regions.
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| 3 June | Jonas Blessing (ETH) Title: Discrete approximation of risk-based prices under volatility uncertainty
Absract: We discuss the asymptotic behaviour of risk-based indifference prices of European contingent claims in discrete-time financial markets under volatility uncertainty as the number of intermediate trading periods tends to infinity. The asymptotic risk-based prices form a strongly continuous convex monotone semigroup which is uniquely determined by its infinitesimal generator and therefore only depends on the covariance of the random factors but not on the particular choice of the model. We further compare the risk-based prices with the worst-case prices given by the G-expectation and investigate their asymptotic behaviour as the risk aversion of the agent tends to infinity. The theoretical results are illustrated with several examples and numerical simulations showing, in particular, that the risk-based prices lead to a significant reduction of the bid-ask spread compared to the worst-case prices.
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| 24 June | Neofytos Rodosthenous (UCL)
Title: Regulation in a mean-field investment game with climate damage
Abstract:We develop a mean-field model of firms investing in carbon-intensive (brown) capital, where productivity declines due to temperature-related climate damages linked to cumulative emissions. Firms aim to maximise expected discounted profits under stochastic capital dynamics driven by idiosyncratic shocks, facing a trade-off between investment-driven growth and increased emissions. We characterise the unique mean-field equilibrium as the solution to a coupled system of forward-backward ordinary differential equations. This framework also enables the analysis of optimal regulatory instruments 鈥� such as carbon emission taxes and brown production phase-out timelines 鈥� in line with long-term climate goals. |
Time and Place:21 April (Tuesday) 11-12 and 14-15; 24 April (Friday) 11-12 and 14-15, in MS04
Anomalous diffusion has been observed in many natural systems, from cellular signalling and animal foraging to contaminant transport in groundwater. This short course consists of two parts. We will first discuss the interplay between anomalous subdiffusions and time-fractional differential equations, including how they arise naturally as scaling limits of random walks. We will then present some recent results, in particular probabilistic representations for solutions of time-fractional equations with source terms. A notable feature is the appearance of two fundamental solutions. We will also discuss applications to scaling limits of trap models and two-sided estimates of fundamental solutions for time-fractional parabolic equations.
There will also be a conference Recent Advances in Stochastic Analysis and Control on 1 May.
Unless otherwise stated the seminars will take place at 11:00am in B3.03 (Zeeman building).
| 18th September MS.05 |
Alfred Chong (Heriot Watt University) Title: Pareto-efficient risk sharing in centralized insurance markets with application to flood risk Abstract: Centralized insurance can be found in both the private and public sectors. This talk provides a microeconomic study of the risk-sharing mechanisms in these markets, where multiple policyholders interact with a centralized monopolistic insurer. With minimal assumptions on the risk preferences of the market participants, we characterize Pareto optimality in terms of the agents' risk positions and their assessment of the likelihoods associated with their loss tail events. We relate Pareto efficiency in this market to a naturally associated cooperative game. Based on our theoretical results, we then consider a model of flood insurance coverage via an illustrative example. The lessons drawn from our theoretical results and this example lead to important policy implications for the existing National Flood Insurance Program in the United States. |
| 2nd October | Internal short presentations from SF@W group members I Leo Baggiani Edward Wang Gechun Liang |
| 9th October | Internal short presentations from SF@W group members II Jo Kennedy Nikolaos Constantinou Vicky Henderson |
| 16th October | Leandro S谩nchez-Betancourt (University of Oxford) Title: Equilibrium between Brokers and Traders Abstract: We study the interactions between a broker and her clients. In the first part of the talk we study the imperfect information case; here, the game is formulated as a two-stage optimisation where both parties filter the information that they do not have. In the second part of the talk we study the perfect information Nash equilibrium. We conclude with an overview of the open problems within this framework. |
| 23rd October | No seminar |
| 30th October | No seminar |
| 6th November | No seminar |
| 13th November | Fay莽al Drissi (University of Oxford) Title: The microstructure of decentralised exchanges Abstract: The bonding curves of decentralised exchanges (DEXs) define, with mathematical formulae, the relationship between liquidity supply, price impact, and execution prices. Most DEXs use the bonding curves of constant function markets (CFMs) to clear the demand and supply of liquidity. CFMs prevent liquidity providers (LPs) from acting strategically, so they operate at a loss, on average. We generalise CFMs and introduce decentralised liquidity pools (DLPs) where dynamic bonding curves maximise the expected wealth of LPs. In the DLP, the bonding curve is determined by impact functions that encode how liquidity taking orders affect prices and by quote functions that encode how the price of liquidity is set. We develop models to find the optimal bonding curve when LTs are sensitive to the price of liquidity and when prices form in a competing trading venue, form in the DLP, or form in various venues. In fragmented markets, the DLP employs the trading flow to estimate the fundamental price and to adjust the bonding curve. Our models may be used as dynamic fee hooks in Uniswap v4 when the price impact of orders are those implied by the constant product function. |
| 20th November | Emmet Lawless (Dublin City University) Title: A variational approach to portfolio choice. Abstract: In this talk we propose a calculus of variations approach to the optimal consumption problem with isoelastic preferences over an infinite horizon. Specifically we consider a complete market with a single state variable on which all model coefficients can depend. Under some mild assumptions we prove the utility maximisation problem is equivalent to solving a tractable, convex variational problem which is far more amenable to numerical methods. This approach circumvents the need to solve the associated Hamilton-Jacobi-Bellman (HJB) equation. This is a desirable situation as explicitly solving the HJB equation is often intractable (even numerical solutions are not necessarily available due to the lack of boundary conditions). We illustrate the utility of this approach by considering a class of models wherein the returns of the risky assets are driven by a non-linear OU type process. Additionally we highlight how this approach may be extended to solve the incomplete market problem. This is joint work with Paolo Guasoni and Ho Man Tai. |
| 27th November | Nazem Khan (University of Oxford) Title: Chain or Channel? Payment Optimization with Heterogeneous Flow Abstract: Compared with existing payment systems, Bitcoin鈥檚 throughput is low. Designed to address Bitcoin鈥檚 scalability challenge, the Lightning Network is a protocol allowing two parties to secure bitcoin payments and escrow holdings between them. Payment-channel networks such as the Lightning Network enable off-chain payments secured by the channels' balances as alternatives to on-chain transactions. This paper solves the optimal channel management problem for two agents who pay each other arbitrarily distributed amounts. Agents optimally choose the channel's size and whether to make each payment on-chain or on-channel, depending on their current balance. This work, in collaboration with Paolo Guasoni, characterizes optimal channels and payment policies, describing an algorithm to obtain them, given payments' frequency and distribution. |
| 4th December | Alessandro Doldi (Universit脿 degli Studi di Milano) Title: Collective arbitrage and dynamic risk measures Abstract: We introduce the notions of Collective Arbitrage and of Collective Super-replication in a discrete-time setting where agents are investing in their markets and are allowed to cooperate through exchanges. We accordingly establish versions of the fundamental theorem of asset pricing and of the pricing-hedging duality. A reduction of the price interval of the contingent claims can be obtained by applying the collective super-replication price. We then explore the implications of cooperation on dynamic risk measurement, focusing particularly on aggregation and time consistency. |
Unless otherwise stated the seminars will take place at 11:00am in B3.03 (Zeeman building).
| 15th January |
Eduardo Abi-Jaber (脡cole Polytechnique) Title: Stochastic Fredholm equations: a passe-partout for propagator models and market impact. Abstract: We will provide explicit solutions to certain systems linear stochastic Fredholm equations. We will then show the versatility of these equations for solving various optimal trading problems with transient impact including: (i) cross-impact (multiple assets), (ii) constraints on the inventory and trading speeds, (iii) N-player game and mean-field interactions (multiple traders). |
| 22nd January | Cosimo Andrea Munari (Universit脿 di Verona) Title: Pricing and exercising American options in a market-consistent way Abstract: We take a fresh look at American options in discrete time and discuss prices and exercise strategies from the point of view of market consistency. This gives a new twist to some known concepts and results. At a technical level, the key results are obtained without resorting to duality. |
| 12th February | Jan Palczewski (University of Leeds) Title Equilibria in zero-sum stopping games with asymmetric information Abstract Zero-sum stopping games (Dynkin games) are a natural generalisation of optimal stopping problems with a well-developed theory for construction of players' strategies. However, when players have access to different information flows (filtrations), little is known. A few specific games have been solved, but the existence of an equilibrium in randomised strategies was only established in 2022. In this talk, I will present our progress towards a general martingale theory for the characterisation of value processes and equilibrium strategies and conclude with an explicitly solvable example. Joint work with Tiziano De Angelis and Jacob Smith. |
| 19th February | TBC |
| 26th February | TBC |
| 12th March | Daniel Lackner (Columbia) --- CANCELLED Title TBC Abstract TBC |
Unless otherwise stated the seminars will take place at 11:00am in B3.03 (Zeeman building).
| 23rd April |
No Seminar |
| 30th April | Peter Tankov (ENSAE) Title: A model of strategic sustainable investment Abstract: We study a problem of optimal irreversible investment and emission reduction formulated as a nonzero-sum dynamic game between an investor with environmental preferences and a firm. The game is set in continuous time on an infinite-time horizon. The firm generates profits with a stochastic dynamics and may spend part of its revenues towards emission reduction (e.g., renovating the infrastructure). The firm's objective is to maximize the discounted expectation of a function of its profits. The investor participates in the profits and may decide to invest to support the firm's production capacity. The investor uses a profit function which accounts for both financial and environmental factors. Nash equilibria of the game are obtained via a system of variational inequalities. We formulate a general verification theorem for this system in a diffusive setup and construct an explicit solution in the zero-noise limit. Our explicit results and numerical approximations show that both the investor's and the firm's optimal actions are triggered by moving boundaries that increase with the total amount of emission abatement. Joint work with Tiziano De Angelis and Caio C茅sar Graciani Rodrigues |
| 7th May | Huy Chau (Manchester) Title: A general framework for pricing and hedging under local viability Abstract: In this talk, a new approach for solving the problems of pricing and hedging derivatives is introduced in a general frictionless market setting. The method is applicable even in cases where an equivalent local martingale measure fails to exist. Our main results include a new superhedging duality for American options when wealth processes can be negative and trading strategies are subject to a cone constraint. This answers one of the questions raised by Fernholz, Karatzas and Kardaras. Joint work with Miklos Rasonyi |
| 14th May | No Seminar |
| 21st May | CRiSM Workshop: No seminar |
| 28th May | Ales Cerny (Bayes Business School) Title: Dynamically optimal portfolios for monotone mean鈥搗ariance preferences Abstract: Monotone mean鈥搗ariance (MMV) utility is the minimal modification of the classical Markowitz utility that respects rational ordering of investment opportunities. This paper provides, for the first time, a complete characterization of optimal dynamic portfolio choice for the MMV utility in asset price models with independent returns. The task is performed under minimal assumptions, weaker than the existence of an equivalent martingale measure and with no restrictions on the moments of asset returns. We interpret the maximal MMV utility in terms of the monotone Sharpe ratio (MSR) and show that the global squared MSR arises as the nominal yield from continuous compounding at the maximal local squared MSR rate. Joint work with Johannes Ruf (LSE) and Martin Schweizer (ETHZ) |
| 4th June | Edward Wang (Warwick)
Nonzero-sum Dynkin games under a generalised order condition: verification theorem and application to convertible bond
Abstract: We consider a two-player nonzero-sum game in continuous time, where the payoffs are not required to satisfy the usual `war of attrition' type order condition. To deal with this non-ordered situation, we provide a verification theorem, which leads to a system of variational inequalities that characterises the payoffs and the strategies of the two players at some Nash equilibria of the game. As an application, we study the problem of convertible bond with tax benefit. In a first example, we obtain multiple nontrivial Nash equilibria. In a second example, we add the additional feature that the bondholder holds two units of convertible bond and may convert them separately. This problem can be modelled as a two-stage nonzero-sum game, and the usual order condition is not satisfied. A Nash equilibrium is found numerically.
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| 11th June | Alex Tse (UCL) Portfolio Selection in Contests In an investment contest with incomplete information, a finite number of agents dynamically trade assets with idiosyncratic risk and are rewarded based on the relative ranking of their terminal portfolio values. We explicitly characterize a symmetric Nash equilibrium of the contest and rigorously verify its uniqueness. The connection between the reward structure and the agents鈥� portfolio strategies is examined. A top-heavy payout rule results in an equilibrium portfolio return distribution with high positive skewness, which suffers from a large likelihood of poor performance. Risky asset holding increases when competition intensifies in a winner-takes-all contest.
The talk is based on joint work with Yumin Lu.
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| 16th June | Joint Seminar with the Gilmore Centre for Finance MS0.4 10am Yuwei Wang
Title:
PreFER: Interactive Robo-Advisor with Scoring Mechanism
Abstract:
Instead of asking a client to specify her risk preference or learning it from her investment choice, we propose an inverse reinforcement learning (IRL) framework to learn her risk preference or the reward function by scoring. Specifically, the robo-advisor requests the client to score unadopted investment advice for improvement, and extracts information from adopted ones for non-interactive periods. We develop the IRL through discrete-time Predictable Forward Exploratory Reward (PreFER) processes, where the exploration is
regularized by Tsallis entropy. By interpreting the score as the acceptance probability of an advice, the preference learning becomes an inverse problem of finding the exploratory investment distribution of the client, given investment distribution recommended by the robo-advisor and an acceptance probability in the context of acceptance-rejection method proposed by Von Neumann. Demonstrations are made for both classes of CARA and CRRA utilities. We prove that the density function of the optimal exploratory control attains maximum at the classic optimal strategy in the absence of exploration. We establish a one-to-one correspondence between the observed score and inferred risk aversion parameter. As long as the scores are consistent in ordering, the biasness of scores does not affect the identification of the client's risk aversion for a sufficient large number of interactions. The PreFER process further predicts the risk preference at the next time point from the one just learned, leading to an aggregation of learning power
11am Hoi Ying Wong (CUHK) Title: Reinforcement learning without a market simulator Abstract:
Reinforcement learning (RL) has found applications in portfolio selection and optimal stopping problems in finance and insurance. Unlike stochastic control problems, which rely on a given stochastic model, an RL agent strikes a balance between exploration and exploitation, where exploration involves randomized decision rules. However, the RL
framework in the finance and insurance literature usually requires a reliable market simulator during the training procedure. While the construction of a market simulator is largely unknown, this limitation restricts applications to high-frequency trading.In this talk, I present two examples of RL that do not require a market simulator but use data other than market prices. The first example focuses on learning efficient investment decisions from liquidity spread data. The exploration aspect of RL enables investors to construct a statistical test for rebalancing time that accounts for liquidity (including transaction) costs. Upon rebalancing, we construct a robust investment rule using exploration with KL divergence regularization.The second example addresses surrendering decisions in variable annuities. The actuarial science literature presents two schools of thought: the optimal surrendering approach based on market information and the surrender intensity approach. Using RL, we demonstrate that the latter can be viewed as an exploratory version of the former. Thus, surrender data can be used to train the RL model for randomized surrender decisions consistent with optimal stopping rules.
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| 18th June | John Armstrong (Kings)
Title: Gamma Hedging Abstract: We will see how the gamma-hedging strategy allows one to replicate derivative contracts without needing to assume any probability model for the underlying. Instead, one needs to assume a pricing model that describes how the hedging instruments vary with the underlying. These results were originally proved using rough-path theory, but we will consider how the proof can be simplified. |
| 4th October 2023
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(WBS) How to choose a model for portfolio selection? A consequentialist approach We propose a consequentialist approach to model selection: Models should be determined not according to statistical criteria, but in view of how they are used. This principle is then studied in detail in the domain of continuous-time portfolio choice. We consider an econometrician with prior beliefs on the likelihood of models to transpire and faced with the task of communicating a single model to an investor. The investor then takes the model communicated by the econometrician and invests according to the strategy maximizing expected utility within this model. The investor receives the consequential performance of trading according to the model communicated by the econometrician in a potentially different model that accurately describes the world. The objective of the econometrician is to choose the model that maximizes the consequential performance of the investor averaged over the likelihood of models to transpire and weighted according to the risk preferences of the econometrician. Our key finding is that it is in the best to communicate a model that is more optimistic than an unbiased estimator would suggest. |
| 11th October 2023 | No seminar. |
| 18th October 2023 |
H枚lder regularity and roughness: Construction and examples We study how to construct a stochastic process on a finite interval with given `roughness' and finite joint moments of marginal distributions. We first extend Ciesielski's isomorphism along a general sequence of partitions, and provide a characterization of H枚lder regularity of a function in terms of its Schauder coefficients. Using this characterization we provide a better (pathwise) estimator of H枚lder exponent. As an additional application, we construct fake (fractional) Brownian motions with some path properties and finite moments of marginal distributions same as (fractional) Brownian motions. These belong to non-Gaussian families of stochastic processes which are statistically difficult to distinguish from real (fractional) Brownian motions. |
| 25th October 2023 | (Imperial College London) Correlated equilibria for mean field games with progressive strategies In a discrete space and time framework, we study the mean field game limit for a class of symmetric N-player games based on the notion of correlated equilibrium. We give a definition of correlated solution that allows to construct approximate N-player correlated equilibria that are robust with respect to progressive deviations. We illustrate our definition by way of an example with explicit solutions. |
| 1st November 2023 | No seminar. |
| 8th November 2023 | (Imperial College London) Ergodic robust maximization of asymptotic growth with stochastic factors We consider an asymptotic robust growth problem under model uncertainty and in the presence of (non-Markovian) stochastic covariance. Building on the previous work of Kardaras & Robertson we fix two inputs representing the instantaneous covariation and invariant density for the asset process X, but additionally allow these quantities to depend on a stochastic factor process Y. Under mild technical assumptions we show that the robust growth optimal strategy is functionally generated and, unexpectedly, does not depend on the factor process Y. Remarkably this remains true even if the joint covariation of X and Y is prescribed as an input. Our result provides a comprehensive answer to a question proposed by Fernholz in 2002. The methods of proof use a combination of techniques from partial differential equations, calculus of variations, and generalized Dirichlet forms. This talk is based on joint work with Benedikt Koch, Martin Larsson and Josef Teichmann. |
| 15th November 2023 | (University of Oxford) Spoofing with Learning Algorithms This paper proposes a dynamic model of the limit order book to derive conditions to test if a trading algorithm will learn to spoof the order book. The testable conditions are simple and easy to implement because they depend only on the parameters of the model. We test the conditions with order book data from Nasdaq and show that market conditions are conducive for an algorithm to learn to spoof the order book. Co-authors: Patrick Chang and Gabriel Garcia-Arenas. |
| 22nd November 2023 | (LSE) Order routing and market quality: Who benefits from internalization? Does retail order internalization benefit, via price improvement, or disadvantage, via reduced liquidity, retail traders? To answer this question, we compare two market designs that differ in their mode of liquidity provision: in the setting capturing retail order internalization liquidity is provided by market makers (representing wholesalers) competing for the retail order flow in a Bertrand fashion. Instead, in the open exchange setting price-taking competitive agents act as liquidity providers. We discover that, when liquidity providers are risk averse, routing of marketable orders to wholesalers is preferred by all retail traders: informed, uninformed and noise. Furthermore, most measures of liquidity are unaffected by the market design. |
| 29th November 2023 | (University College London) Non-zero-sum optimal stopping game with continuous versus periodic exercise opportunities We introduce a new non-zero-sum game of optimal stopping with asymmetric exercise opportunities. Given a stochastic process modelling the value of an asset, one player observes and can act on the process continuously, while the other player can act on it only periodically at independent Poisson arrival times. The first one to stop receives a reward, different for each player, while the other one gets nothing. We study how each player balances the maximisation of gains against the maximisation of the likelihood of stopping before the opponent. In such a setup, driven by a L茅vy process with positive jumps, we prove the existence as well as explicitly construct a Nash equilibrium. Joint work with Jose Luis Perez and Kazutoshi Yamazaki. |
| 6th December 2023 | (University of Liverpool) This talk is postponed to Term 2. |
| 13th December 2023 Room MS.04 |
(University of Oxford) Mean-Field Approximations in Heterogeneous N-Player Games Mean-field games (MFGs) offer a valuable approach to approximating and analyzing the challenging N-player stochastic games. However, existing literature primarily addresses approximation errors in MFGs and N-player games when players are permutation invariant. The rate of convergence remains undetermined for general N-player games. This talk addresses this gap by presenting the first non-asymptotic approximation results for multi-population MFGs (MP-MFGs) compared to heterogeneous N-player games. We initiate our exploration with mean-field type N-player games, featuring K groups of identical and permutation-invariant players. Notably, we establish non-asymptotic approximation error bounds without assuming the uniqueness of Nash equilibrium solutions. The analysis then extends to generic heterogeneous N-player games, encompassing variations in rewards, transition probabilities, and interactions among players that go beyond mean-field type scenarios./td> |
| 31st January 2024
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Miha Bresar (Warwick) Superdiffusive limits for Bessel-driven stochastic kinetics We explore the scaling of anomalous diffusion in a one-dimensional stochastic kinetic dynamics model. Our model features stochastic drift influenced by external Bessel noise and incorporates internal volatility, which has an arbitrary relationship with this external noise. We identify the superdiffusive scaling exponent for the model, and prove a weak convergence result on the corresponding scale. We show how our result extends to admit, as exogenous noise processes, not only Bessel processes but more general processes satisfying certain asymptotic conditions. We conclude by exploring the connections with stochastic interest rate models. This talk is based on joint work with Conrado Da Costa, Aleks Mijatovi膰 and Andrew Wade. |
| 7th February 2024 |
Radner equilibrium and systems of quadratic BSDEs with discontinuous generators We establish the existence of a Radner Equilibrium in an incomplete, continuous-time financial economy. To prove existence, we formulate a system of quadratic backward stochastic differential equations (BSDEs) which represents the equilibrium problem. Interestingly, the driver of this system of BSDEs features a discontinuity, posing a major challenge for common approaches to establish existence. Exploiting the duality between Markovian BSDEs and PDEs we use unique continuation and backward uniqueness, techniques originally used in the study of PDEs, to show that the set of discontinuity has in fact measure zero. (Joint work with Luis Escauriaza and Hao Xing.) |
| 21st February 2024 | (Liverpool) Trapping Probability in Low-Income Household Capital Dynamics: Insurance and Subsidies Impact We are examining a risk process characterized by deterministic growth and multiplicative jumps to represent the capital dynamics of low-income households. To account for the higher risk inherent in such environments, we assume that capital losses are proportional to the level of accumulated capital at the time of a jump. Our objective is to calculate the probability of a household falling below the poverty line, known as the trapping probability. "Trapping" arises when a household's capital falls below the poverty threshold, creating a situation from which escape without external help is not possible. We approach the remaining capital distribution as specific instances of the beta distribution and derive closed-form expressions for the trapping probability by analyzing the Laplace transform of the process' infinitesimal generator. Additionally, we investigate the impact of insurance on this probability, particularly when the insurance product provides proportional coverage. Our findings suggest that in certain scenarios, trapping is inevitable without external aid, typically provided in the form of subsidies. |
| 28th February 2024 | (Durham) Rough Stochastic Analysis with Jumps Rough path theory provides a framework for the study of nonlinear systems driven by highly oscillatory (deterministic) signals. The corresponding analysis is inherently distinct from that of classical stochastic calculus, and neither theory alone is able to satisfactorily handle hybrid systems driven by both rough and stochastic noise. The introduction of the stochastic sewing lemma (Khoa L锚, 2020) has paved the way for a theory which can efficiently handle such hybrid systems. In this talk, we will discuss how this can be done in a general setting which allows for jump discontinuities in both sources of noise. |
| 13 March 2024 | Lecture series by (Columbia) More information can be found on this webpage . |
| 1st May 2024
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(Imperial College London) Global solutions for stochastically controlled models Abstract: For a class of evolution equations that possibly have only local solutions, we introduce a stochastic component that ensures that the solutions of the corresponding stochastically perturbed equations are global. The class of partial differential equations amenable for this type of treatment includes the 3D Navier-Stokes equation, the rotating shallow water equation (viscous and inviscid), 3D Euler equation (in vorticity form), 2D Burgers' equation and many other fluid dynamics models. This is based on joint work with Oana Lang (Babes-Bolyai University). |
| 8th May 2024 |
(Queen Mary University of London) Optimal stopping with nonlinear expectation: geometric and algorithmic solutions We use the geometry of functions associated with martingales under nonlinear expectations to solve risk-sensitive Markovian optimal stopping problems. Generalising the linear case due to Dynkin and Yushkievich (1969), the value function is the majorant or pointwise infimum of those functions which dominate the gain function. An emphasis is placed on the geometry of the majorant and pathwise arguments, rather than exploiting convexity, positive homogeneity or related analytical properties. An algorithm is provided to construct the value function at the computational cost of a two-dimensional search. The talk is based on the preprint https://arxiv.org/abs/2306.17623 (with Tomasz Kosmala). |
| 15th May 2024 MS.02 |
(University of Vienna) Functional It么 formula and Taylor expansion for non-anticipative maps of rough paths: We rely on the approximation properties of the signature of c脿dl脿g rough paths to derive a functional It么 formula for non-anticipative maps of rough paths. This leads to a functional extension of the It么 formula for c脿dl脿g rough paths (by Friz and Zhang (2018)) which coincides with the change of variable formula formulated by Dupire (2009) as well as by Cont and Fournie (2010), whenever the notions of the regularity of the functionals and the integration coincide. As a byproduct, we show that sufficiently regular non-anticipative path functionals admit a functional Taylor expansion, leading to a far reaching generalization of the recently established results by Dupire and Tissot-Daguette (2022). The talk is based on ongoing joint work with Xin Guo and Francesca Primavera. |
| 29th May 2024 NEW ROOM MB0.08 |
Aria Ahari (天美传媒) Boundary crossing problems and functional transformations for Ornstein-Uhlenbeck processes. We are interested in the law of the first passage time of an Ornstein-Uhlenbeck process to time-varying thresholds. We show that this problem is connected to the laws of the first passage time of the process to members of a two-parameter family of functional transformations of a time-varying boundary. For specific values of the parameters, these transformations appear in a realisation of a standard Ornstein-Uhlenbeck bridge. We provide three different proofs of this connection. The first one is based on a similar result for Brownian motion, the second uses a generalisation of the so-called Gauss-Markov processes and the third relies on the Lie group symmetry method. We investigate the properties of these transformations and study the algebraic and analytical properties of an involution operator which is used in constructing them. We also show that these transformations map the space of solutions of Sturm-Liouville equations into the space of solutions of the associated nonlinear ordinary differential equations. Lastly, we interpret our results through the method of images and give new examples of curves with explicit first passage time densities. This is joint work with my supervisors Dr. Larbi Alili and Dr.Massimiliano Tamborrino. Link to the pre-print: |
| 19th June 2024 MB0.08 Wilfried Kuissi-Kamdem (AIMS Ghana/University of Rwanda) Pricing and hedging of (path-dependent) claims based on non-tradable assets for Epstein-Zin utility We present an Epstein-Zin utility indifference pricing and hedging for multidimensional tradable and non-tradable assets models. We provide an explicit expression for the utility indifference prices and their corresponding derivative hedges. Using forward-backward SDE method and Malliavin calculus, in a possibly non-Markovian diffusion model for the financial market, a linear indifference pricing rule is obtained. We apply our methodology to the pricing and hedging of weather derivatives, crack spread options, variance swaps, volatility swaps and options on levered exchange traded funds. (This talk is based on ongoing joint work with Olivier Menoukeu Pamen and Marcel Ndengo) |
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| 21st June 2024 Joint Session with the Guillmore Centre for Financial Technology WBS Teaching Centre 2:00-3:30pm Please note that registration is required. |
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| 3rd July 2024 Room MB0.02 Min Dai Equilibrium Mean-Variance Strategy with Transaction Costs We study continuous-time mean-variance portfolio selection in the presence of proportional transaction costs, which can be formulated as a time-inconsistent singular stochastic control problem. We provide a novel definition of equilibrium solutions for the singular control problem and characterize them by a system of HJB equations. We reveal that the standard mean-variance criteria with a constant risk preference may yield absurd equilibrium strategies in the presence of transaction costs. We find that a time-varying risk preference yields a reasonable and stable equilibrium strategy. This work is jointly with Yanwei Jia and Hanqing Jin. |
| 29th September B 3.02 (Zeeman) |
Mihail Zervos (London School of Economics) Risk Sharing with Mean-Variance Preferences and Proportional Transaction Costs We consider an economy with two agents. Each of the two agents receives a random endowment flow. We model this cumulative flow as the the stochastic integral of a deterministic function of the economy's state, which we model by means of a general Ito diffusion. Each of the two agents has mean-variance preferences with different risk-aversion coefficients. To hedge against the random fluctuations of their individual endowments, the two agents may enter a risk-sharing agreement to trade a risky asset that is in zero net supply. We determine the agents' optimal equilibrium trading strategies in the presence of proportional transaction costs. In particular, we derive a new free-boundary problem that provides the solution to the agents' optimal equilibrium problem. Furthermore, we derive the explicit solution to this free-boundary problem when the problem data is such that the frictionless optimiser is a strictly increasing or a strictly increasing and then strictly decreasing function of the economy's state. |
| 6th October |
Michael Kupper (Universit盲t Konstanz) Nonlinear semigroups and limit theorems for convex expectations Motivated by model uncertainty, we focus on semigroups of convex monotone operators on spaces of continuous functions. In contrast to the linear theory, the domain of the generator is not invariant. In order to overcome this issue, we consider so-called Lipschitz sets which turn out to be a suitable domain for a weaker notion of the generator. This is defined using Gamma-convergence in an appropriate function space. We show that the Gamma-generator uniquely characterizes the nonlinear semigroup. In particular, we obtain that different approximation schemes lead to the same semigroup. As an application of our results, we show that LLN and CLT type results for convex expectations can be systematically obtained by the so-called Chernoff approximation. The talk is based on joint work with Jonas Blessing, Robert Denk and Max Nendel. |
| 3rd November | Leandro Sanchez-Betancourt (King's College London) Internalise or Externalise: Brokers and Informed Trading We study how a broker provides liquidity to an informed trader and to a noise trader. The broker decides how much of the flow she keeps in her books (i.e., internalisation) and how much she unwinds in an exchange (i.e., externalisation). We frame the interactions between the broker and traders as a Stackelberg game. The informed trader knows the stochastic process that drives the drift of the asset price. The order flow of the noise trader is uninformative. We obtain the broker's internalisation and externalisation optimal strategy in closed-form. We show the performance of the broker, the noise trader, and the informed trader for a variety of scenarios. Lastly, we compute the amount of transaction costs that the broker needs to charge to break even. |
| 10th November | Alexandre Pannier (LPSM Paris) On the ergodic behaviour of affine Volterra processes We show the existence of a stationary measure for a class of multidimensional stochastic Volterra systems of affine type. These processes are in general not Markovian, a shortcoming which hinders their large-time analysis. We circumvent this issue by lifting the system to a measure-valued stochastic PDE introduced by Cuchiero and Teichmann, whence we retrieve the Markov property. Leveraging on the associated generalised Feller property, we extend the Krylov-Bogoliubov theorem to this infinite-dimensional setting and thus establish an approach to the existence of invariant measures. We present concrete examples, including the rough Heston model from Mathematical Finance. |
| 1st December | Alex Tse (University College London) Periodic portfolio selection with quasi-hyperbolic discounting In this talk, I will introduce a continuous-time portfolio selection problem faced by an agent with S-shaped preference who maximises the discounted utilities derived from the portfolio's periodic performance over an infinite horizon. I will first briefly outline the solution method under a baseline exponential discounting setup. Then I will introduce a time-inconsistent version of the problem featuring quasi-hyperbolic discounting where multiple notions of optimality arise. If the agent is sophisticated who seeks a consistent planning strategy, the problem can then be analysed via a static mean field game where theoretical characterisation of the optimal strategy is provided. |
| 1st February 2023
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(Dublin City University) General Equilibrium with Unhedgeable Fundamentals and Heterogeneous Agents We solve a general equilibrium model in which aggregate consumption has uninsurable growth shocks, rendering the market dynamically incomplete. Several long-lived agents with heterogeneous risk-aversion and time-preference make consumption and investment decisions, trading risky assets and borrowing from and lending to each other. For small growth fluctuations, we obtain closed-form expressions for stock prices, interest rates, and consumption and trading policies. Agents' stochastic discount factors depend on the history of unhedgeable shocks, agents trade assets dynamically, and the dispersion of agents' preferences impacts both the interest rate and asset prices, hence no representative agent exists. |
| 15th February 2023 |
(Universit茅 de Bordeaux) BSDEs reflected in a non convex domain: a geometric point of view In a recent paper, we have proved, with J.-F. Chassagneux and S. Nadtochiy, some existence and uniqueness results for BSDEs reflected in a non-convex domain under some restrictive assumptions on the domain and the terminal condition. All these results were obtained by tools and estimates based on the Euclidean structure of $\mathbb{R}^d$. In order to improve these results, at least in dimension $2$, it is also possible to see our domain as a flat manifold with a boundary and to take advantage of geometry tools already developed to tackle martingales in (non flat) manifolds (without boundary). In this talk, I will explain this new approach and the kind of results we are able to obtain. This is a work in progress with M. Arnaudon, J.-F. Chassagneux and S. Nadtochiy. |
| 22nd February 2023 | David Bang (天美传媒) Coupling of multidimensional L茅vy processes and Wasserstein bounds in the small time stable domain of attraction We establish upper and lower bounds on the rate of convergence of the Wasserstein distance on the path space for a wide class of L茅vy processes attracted to a multidimensional stable law in the small-time regime. In this talk, the main focus will be on the development of two novel couplings between arbitrary pure-jump L茅vy processes, used to obtain upper bounds on the Wasserstein distance. We show that the rate of convergence is polynomial for the domain of normal attraction and slower than any polynomial for the domain of non-normal attraction. As an example, we will consider the class of tempered stable processes that are in the small time domain of attraction of a stable process. |
| 1st March 2023 | (University of Liverpool) Optimal consumption with labour income and borrowing constraints for recursive preferences In this talk, we present an optimal consumption and investment problem for an investor with liquidity constraints who has isoelastic recursive Epstein-Zin utility preferences and receives a stochastic stream of income. We characterise the optimal consumption strategy as well as the terminal wealth for recursive utility under dynamic liquidity constraints, which prevent the investor to borrow against his stochastic future income. Using duality and backward SDE methods in a possibly non-Markovian diffusion model for the financial market, this gives rise to an interplay of singular control and optimal stopping problems. This talk is based on a joint work with D. Becherer and W. D. Kuissi Kamdem. |
| 8th March 2023 | Xin Zhi (天美传媒) Optimal Stopping with Trees In this talk, we will first review a recent method for solving high-dimensional optimal stopping problems using deep Neural Networks. Second, we propose an alternative algorithm replacing Neural Networks by CART-trees which allow for more interpretation of the estimated stopping rules. We apply our algorithm to multiple examples. We in particular compare the performance of the two algorithms with respect to the Bermudan max-call benchmark example. We also show how our algorithm can be used to plot stopping boundaries. |
| 15th March 2023 /cancelled/ /will be rescheduled/ |
(University College London) Radner equilibrium and systems of quadratic BSDEs with discontinuous generators We establish the existence of a Radner Equilibrium in an incomplete, continuous-time financial economy. To prove existence, we formulate a system of quadratic backward stochastic differential equations (BSDEs) which represents the equilibrium problem. Interestingly, the driver of this system of BSDEs features a discontinuity, posing a major challenge for common approaches to establish existence. Exploiting the duality between Markovian BSDEs and PDEs we use unique continuation and backward uniqueness, techniques originally used in the study of PDEs, to show that the set of discontinuity has in fact measure zero. (Joint work with Luis Escauriaza and Hao Xing.) /This talk has been cancelled and will be rescheduled in Term 3/ |
| 3rd May 2023
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(Imperial College London) Optimality and Statistical Learning of Propagator Models Price impact refers to the empirical fact that execution of a large order affects the risky asset's price in an adverse and persistent manner leading to less favourable prices. Propagator models help us to quantity the price impact. They express price moves in terms of the influence of past trades, convoluted with a price impact kernel function. We consider a class of optimal liquidation problems where the agent's transactions create transient price impact driven by a Volterra-type propagator along with temporary price impact. We formulate these problems as minimization of a revenue-risk functionals, where the agent also exploits available information on a progressively measurable price predicting signal. By using an infinite dimensional stochastic control approach, we derive analytic solutions to these equations which yields an explicit expression for the optimal trading strategy. We then consider a class of learning problems in which an agent liquidates a risky asset while creating transient price impact driven by an unknown propagator. We characterize the trader's performance as maximization of a revenue-risk functional, where the trader also exploits available information on a price predicting signal. We present a trading algorithm that alternates between exploration and exploitation phases and achieves sublinear regrets with high probability. For the exploration phase we propose a novel approach for non-parametric estimation of the price impact kernel by observing only the visible price process and derive sharp bounds on the convergence rate, which are characterised by the singularity of the propagator. |
| 10th May 2023
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(Bielefeld University) A Parametric Approach to the Estimation of Convex Risk Functionals based on Wasserstein Distance We explore a static setting for the assessment of risk in the context of mathematical finance and actuarial science that takes into account model uncertainty in the distribution of a possibly infinite-dimensional risk factor. We allow for perturbations around a baseline model, measured via Wasserstein distance, and we investigate to which extent this form of probabilistic imprecision can be parametrized. The aim is to come up with a convex risk functional that incorporates a safety margin with respect to nonparametric uncertainty and still can be approximated through parametrized models.The particular form of the parametrization allows to develop a numerical method, based on neural networks, which gives both the value of the risk functional and the optimal perturbation of the reference measure. Moreover, we study the problem under additional constraints on the perturbations, namely, a mean and a martingale constraint. We show that, in both cases, under suitable conditions on the loss function, it is still possible to estimate the risk functional by passing to a parametric family of perturbed models, which again allows for a numerical approximation via neural networks. The talk is based on joint work with Alessandro Sgarabottolo. |
| 24th May 2023 Room MS.04 |
(LSE) Speeding up the Euler scheme for killed diffusions Let X be a linear diffusion taking values in (l,r) and consider the standard Euler scheme to compute an approximation to E[g(X(T);T<u]] for="" a="" given="" function="" g="" and="" deterministic="" t,="" where="" u="" is="" the="" first="" time="" that="" x="" exits="" (l.r).="" it="" well-known="" presence="" of="" killing="" introduces="" loss="" accuracy..="" we="" introduce="" drift-implicit="" euler="" method="" to="" bring="" convergence="" rate="" back="" optimal="" can="" be="" obtained="" in="" absence="" killing,="" using="" theory="" recurrent="" transformations="" developed="" recently.="" although="" current="" setup="" assumes="" one-dimensional="" setting,="" multidimensional="" extension="" within="" reach="" as="" soon="" systematic="" treatment="" available="" higher="" dimensions.<="" p=""> </u]]> |
| 21st June 2023 Room MS.03 |
(Essex) Measures of Risk under Uncertainty A risk analyst assesses potential financial losses based on multiple sources of information. Often, the assessment does not only depend on the specification of the loss random variable, but also various economic scenarios. Motivated by this observation, we design a unified axiomatic framework for risk evaluation principles which quantifies jointly a loss random variable and a set of plausible probabilities. We call such an evaluation principle a generalized risk measure and present a series of relevant theoretical results. The worst-case, coherent, and robust generalized risk measures are characterized via different sets of intuitive axioms. We establish the equivalence between a few natural forms of law invariance in our framework, and the technical subtlety therein reveals a sharp contrast between our framework and the traditional one. Moreover, coherence and strong law invariance are derived from a combination of other conditions, which provides additional support for coherent risk measures such as Expected Shortfall over Value-at-Risk, a relevant issue for risk management practice. |
| 14th July 2023 (On Friday) Room MS.03 |
(Oxford) Stability and approximation of projection filters Nonlinear filtering is a central mathematical tool in understanding how we process information. Sadly, the equations involved are often very high dimensional, which may lead to difficulties in applications. One possible resolution (due to D. Brigo and collaborators) is to replace the filter by a low-dimensional approximation, with hopefully small error. In this talk we will see how, in the case where the underlying process is a finite-state Markov Chain, results on the stability of filters can be strengthened to show that this introduces a well-controlled error, leveraging tools from information geometry. (Based on joint work with Eliana Fausti) |
| 15th Oct 2021 | Nazem Khan (天美传媒) Sensitivity to large losses and |
| Thu 4th Nov 2021, 2pm (online only) |
Matteo Burzoni (Universit脿 degli Studi di Milano) Mean Field Games with absorption and a model of bank runLink opens in a new window |
| 26th Nov 2021 11am in L3 (Science Concourse) |
Johannes Muhle-Karbe (Imperial College London) Hedging with Market and Limit OrdersLink opens in a new window |
| 3rd Dec 2021, 11am (online only) |
Roxana Dumitrescu (King's College London) |
| 4th Feb 2022 | Ruiqi Liu (天美传媒) |
| 25th Feb 2022 (online only) |
Huy Chau (University of Manchester) |
| 18th Mar 2022 (online only) |
Mikko Pakkanen (Imperial College London) |
| 26th May 2022 | Harto Saarinen (University of Turku) |
| 9th June 2022 | Urvashi Behary Paray (天美传媒) Convexity Corrections via a Markov-functional approachLink opens in a new window |
| Wed 15th June 2022 3pm in MS.04 |
Cosimo Andrea Munari (University of Zurich) |
| 16 Oct 2020 | (University of Waterloo) |
| An axiomatic foundation for the Expected ShortfallLink opens in a new window | |
| 23 Oct 2020 | () |
| Forward Rank-Dependent Performance Criteria: Time-Consistent Investment Under Probability Distortion |
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| 30 Oct 2020 | Jorge Gonzalez CazaresLink opens in a new window (Warwick) |
| Monte Carlo methods for the extrema of Levy models | |
| 13 Nov 2020 | (Columbia University) |
| Local stochastic volatility models and inverting the Markovian projection | |
| 20 Nov 2020 | (Columbia University) |
| Liquidity Risk and Asset Pricing | |
| 27 Nov 2020 | Joseph JeromeLink opens in a new window (Warwick) |
| Infinite Horizon Stochastic Differential Utility |
| 29 Jan 2021 | (Universit茅 de Paris) |
| Modeling carbon markets using Forward-Backward SDEs | |
| 2 Feb 2021 (unusual time!) | (Oxford University) |
| Deep neural network approximations to stochastic control problems | |
| 12 Feb 2021 | (Le Mans Universit茅) |
| Mean-field reflected backward stochastic differential equations | |
| 19 Feb 2021 | (Yale University) |
| Optimal Financial Transaction Taxes | |
| 26 Feb 2021 | (University of Miami) |
| Optimal Consumption under a Habit-Formation Constraint | |
| 5 Mar 2021 | (ETH) |
| Time-inconsistent control and backward integral Volterra SDEs |
| 28 April 2021 (3-4PM) | (University of Michigan) |
| Department Colloquium | |
| 7 May 2021 | (Osaka University) |
| Volatility has to be rough | |
| 14 May 2021 | (Hong Kong Polytechnic University) |
| An Optimal Investment Problem with Nonsmooth and Nonconcave Utility over a Finite Time Horizon | |
| 21 May 2021 | (University of Leeds) |
| Pricing and hedging of options in non-linear incomplete financial market modelsLink opens in a new window | |
| 28 May 2021 | (Bielefeld University) |
| TWO-SIDED SINGULAR CONTROL OF AN INVENTORY WITH UNKNOWN DEMAND TREND | |
| 4 June 2021 | (University of Jena) |
| The De Vylder-Goovaerts conjecture holds true within the diffusion limit |
| 18.10.2019 | John Armstrong (Kings College London) |
| Isomorphisms of Markets | |
| 08.11.2019 | Renyuan Xu (Oxford University) |
| A Case Study on Pareto Optimality for Collaborative Stochastic GamesLink opens in a new window | |
| 15.11.2019 | Eric Renault (Univeristy of Warwick) |
| Identification-Robust Inference for Risk Prices in Structural Stochastic Volatility ModelsLink opens in a new window | |
| 22.11.2019 | Andreas Kyprianou (University of Bath) |
| Entrance and exit at infinty for stable jump diffusionsLink opens in a new window | |
| 29.11.2019 | Miryana Grigorova (University of Leeds) |
| A non-linear incomplete market model with default: Pricing of European and American options |
| 24.01.2020 | Ernst Eberlein (University of Freiburg) | |
| Multiple curve interest rate modellingLink opens in a new window | ||
| 21/02/2020 |
Daniela Escobar (London School of Economics) | |
| Robust pricing for insurance contracts, dynamic problems and possible extensions | ||
| 13/03/2020 |
Drik Becherer (Humboldt University of Berlin) |
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| Optimal trade execution with transient relative price impact and directional views: A variational approach to a 3-dimensional non-convex free boundary problem |
| 12.10.2018 | Teemu Pennanen (King's College London) |
| Convex duality in nonlinear optimal transport | |
| 19.10.2018 | Tiziano De Angelis (University of Leeds) |
| Dynkin games with incomplete and asymmetric information | |
| 1-2.11.2018 | Fudan-Warwick Workshop on Financial Mathematics and Stochasitc Analysis |
| 23.11.2018 | Alexander Cox (University of Bath) |
| Utility Maximisation with Model-Independent Trading Constraints | |
| 30.11.2018 | Sigrid K盲llblad (Vienna University of Technology) |
| Stochastic control of measure-valued martingales with applications to robust pricing and Skorokhod embedding problems |
| 18.01.2019 | Alex Mijatovic (天美传媒) |
| Stability of overshoots of zero mean random walks | |
| 25.01.2019 | Michael Tehranchi (University of Cambridge) |
| A Black--Scholes inequality: Applications and generalisations |
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| 01.02.2019 | Neofytos Rodosthenous (Queen Mary University of London) |
| Optimal timing for governmental control of the debt-to-GDP ratio | |
| 15.02.2019 | Matija Vidmar (University of Ljubljana) |
| On a family of non-linear optimal martingale transport problems |
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| 22.02.2019 | Mihail Zervos (LSE) |
| Risksharing with two-sided limited commitment: a duality approach in continuous time |
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| 01.03.2019 | Athena Picarelli (University of Verona) |
| Optimal control under controlled loss constraints via reachability approach and compactification |
|
| 05.04.2019 | Daniel Bartl (University of Vienna) |
| Model uncertainty in mathematical finance via Wasserstein distances |
| 24.05.2019 | Peter Tankov (ENSAE ParisTech) |
| Mean-field games of optimal stopping and industry dynamics in the electricity market | |
| 07.06.2019 | Jukka Lempa (University of Turku) |
| A Class of Solvable Multiple Entry Problems with Forced Exits | |
| 14.06.2019 | Roxana Dumitrescu (King's College London) |
| A dynamic dual representation of the buyer's price of American options in a nonlinear |
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| 21.06.2019 | Frank Riedel (Bielefeld University) |
| Viability and Arbitrage under Knightian Uncertainty | |
| 28.06.2019 | Christoph Czichowsky (LSE) |
| Rough volatility and portfolio optimisation under transaction costs |
| 27.10.2017 | Andreea Minca (Cornell) |
| Systemic Risk and Central Clearing Counterparty Design | |
| 17.11.2017 | Michalis Anthropelos (Piraeus) |
| Equilibrium Transactions with large investors and indifferent market makers | |
| 24.11.2017 |
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| cancelled | |
| 01.12.2017 | Samuel Cohen (Oxford) |
| Uncertainty in Kalman-Bucy Filtering | |
| 08.12.2017 | Yiqing Lin (脡cole Polytechnique) |
| Second-order Backward SDEs with Random Terminal Time |
| 12.01.2018 | Ying Hu (Rennes) |
| Multidimensional (Backward) Stochastic Differential Equations with Constraints on Law | |
| 19.01.2018 | Dmitrii Lisovskii (Moscow State) |
| Sequential Problems for a Brownian Bridge | |
| 02.02.2018 | Peiran Jiao (Maastricht) |
| Signal Processing on Social Media: Theory and Evidence from Financial Markets | |
| 09.02.2018 | Samuel Drapeau (Shanghai Jiao Tong) |
| Computational Aspects of Robust Optimized Certainty Equivalent | |
| 09.03.2018 | S枚ren Christensen (Hamburg) |
| Non-Smooth Verification for Impulse Control Problems | |
| 16.03.2018 | D枚rte Kreher (HU Berlin) |
| First and second order approximations for a Markovian limit order book model |
| 04.05.2018 11am | Hao Xing (LSE) |
| Optimal contracting with unobservable managerial hedging | |
| 04.05.2018 2pm | Sebastian Herrmann (Michigan) |
| Inventory Management for High-Frequency Trading with Imperfect Competition | |
| 11.05.2018 | Thaleia Zariphopoulou (Austin) |
| Mean-field and n-agent games for optimal investment under relative performance criteria | |
| 25.05.2018 | Florian Stebegg (Columbia) |
| Strong Duality and Relaxations in Constrained Transport | |
| 15.06.2018 | Peter Austing (Citadel) |
| Model-free Valuation of Barrier Options | |
| 29.06.2018 | Cosimo Andrea-Munari (窜眉谤颈肠丑) |
| Existence, uniqueness and stability of optimal portfolios of eligible assets |
| 21.10.2016 | Blanka Horvath (Imperial) |
| Aspects of asymptotic expansions in fractional volatility models | |
| 04.11.2016 | Tiziano De Angelis (Leeds) |
| The dividend problem with a finite horizon | |
| 11.11.2016 | Thomas Cay茅 (ETH Z眉rich) |
| Trading with small nonlinear price impact | |
| 25.11.2016 | Frank Kelly (Cambridge) |
| A Markov model of a limit order book: thresholds, recurrence, and trading strategies | |
| 02.12.2016 | Saul Jacka (Warwick) |
| General Controlled Markov Processes and Optimal Stopping |
| 20.01.2017 | Christoph Czichowsky (LSE) |
| Portfolio Optimisation, Transaction Costs, Shadow Prices and Fractional Brownian Motion | |
| 10.03.2017 | Daniel Schwarz (UCL) |
| The existence of densities of BSDEs | |
| 17.03.2017 | Frank Seifried (Trier) |
| Epstein-Zin Stochastic Differential Utility | |
| 05.05.2017 | Paolo Guasoni (Dublin City) |
| Leveraged Funds: Robust Replication and Performance Evaluation | |
| 19.05.2017 | Luciano Campi (LSE) |
| N-player games and mean field games with absorption | |
| 26.05.2017 | Sebastian Herrmann (Michigan) |
| Robust Pricing and Hedging around the Globe | |
| 09.06.2017 | Bruno Bouchard (Paris Dauphine) |
| Super-hedging with proportional transaction costs under uncertainty : a randomization approach | |
| 23.06.2017 | Johannes Muhle-Karbe (Michigan) |
| A Risk-Neutral Equilibrium Leading to Uncertain Volatility Pricing |