Stochastic Finance @ Warwick Seminars
Unless otherwise stated the seminars will take place at 11:00am in B3.03 (Zeeman building). If you have any question, please contact the seminar organiser Martin HerdegenLink opens in a new window.
18th September MS.05 
Alfred Chong (Heriot Watt University) Title: Paretoefficient 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 risksharing 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 SánchezBetancourt (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 twostage 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  Fayçal 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: TBC Abstract: TBC 
27th November  Nazem Khan (University of Oxford) Title: TBC Abstract: TBC 
4th December  Alessandro Doldi (Università degli Studi di Milano) Title: TBC Abstract: TBC 
Unless otherwise stated the seminars will take place at 11:00am in B3.03 (Zeeman building). If you have any question, please contact the seminar organiser Martin HerdegenLink opens in a new window.
15th January 
Eduardo AbiJaber (École Polytechnique) Title: TBC Abstract: TBC 
22nd January  TBC 
29th January  TBC 
5th February  TBC 
12th February  TBC 
19th February  TBC 
26th February  TBC 
5th March  TBC 
12th March  TBC 
19th March  TBC 
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4th October 2023

Moris StrubLink opens in a new window (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 continuoustime 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  Purba Das (King's College London) Hölder 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 Hölder regularity of a function in terms of its Schauder coefficients. Using this characterization we provide a better (pathwise) estimator of Hölder 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 nonGaussian families of stochastic processes which are statistically difficult to distinguish from real (fractional) Brownian motions. 
25th October 2023  Ofelia Bonesini (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 Nplayer games based on the notion of correlated equilibrium. We give a definition of correlated solution that allows to construct approximate Nplayer 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  David Itkin (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 (nonMarkovian) 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  Alvaro Cartea (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. Coauthors: Patrick Chang and Gabriel GarciaArenas. 
22nd November 2023  Albina Danilova (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 pricetaking 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  Neofytos Rodosthenous (University College London) Nonzerosum optimal stopping game with continuous versus periodic exercise opportunities We introduce a new nonzerosum 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 Lévy 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  Corina Constantinescu (University of Liverpool) This talk is postponed to Term 2. 
13th December 2023 Room MS.04 
Anran Hu (University of Oxford) MeanField Approximations in Heterogeneous NPlayer Games Meanfield games (MFGs) offer a valuable approach to approximating and analyzing the challenging Nplayer stochastic games. However, existing literature primarily addresses approximation errors in MFGs and Nplayer games when players are permutation invariant. The rate of convergence remains undetermined for general Nplayer games. This talk addresses this gap by presenting the first nonasymptotic approximation results for multipopulation MFGs (MPMFGs) compared to heterogeneous Nplayer games. We initiate our exploration with meanfield type Nplayer games, featuring K groups of identical and permutationinvariant players. Notably, we establish nonasymptotic approximation error bounds without assuming the uniqueness of Nash equilibrium solutions. The analysis then extends to generic heterogeneous Nplayer games, encompassing variations in rewards, transition probabilities, and interactions among players that go beyond meanfield type scenarios./td> 
31st January 2024

Miha Bresar (Warwick) Superdiffusive limits for Besseldriven stochastic kinetics We explore the scaling of anomalous diffusion in a onedimensional 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 Mijatović 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, continuoustime 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  Corina Constantinescu (Liverpool) Trapping Probability in LowIncome 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 lowincome 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 closedform 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  Andrew Allan (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 Lê, 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 Ioannis Karatzas (Columbia) More information can be found on this webpage . 
1st May 2024

Dan Crisan (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 NavierStokes 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 (BabesBolyai University). https://arxiv.org/abs/2403.05923 
8th May 2024 
John Moriarty (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 risksensitive 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 twodimensional search. The talk is based on the preprint https://arxiv.org/abs/2306.17623 (with Tomasz Kosmala). 
15th May 2024 MS.02 
Christa Cuchiero (University of Vienna) Functional Itô formula and Taylor expansion for nonanticipative maps of rough paths: We rely on the approximation properties of the signature of càdlàg rough paths to derive a functional Itô formula for nonanticipative maps of rough paths. This leads to a functional extension of the Itô formula for càdlàg 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 nonanticipative path functionals admit a functional Taylor expansion, leading to a far reaching generalization of the recently established results by Dupire and TissotDaguette (2022). The talk is based on ongoing joint work with Xin Guo and Francesca Primavera. 
29th May 2024 NEW ROOM MB0.08 
Aria Ahari (University of Warwick) Boundary crossing problems and functional transformations for OrnsteinUhlenbeck processes. We are interested in the law of the first passage time of an OrnsteinUhlenbeck process to timevarying thresholds. We show that this problem is connected to the laws of the first passage time of the process to members of a twoparameter family of functional transformations of a timevarying boundary. For specific values of the parameters, these transformations appear in a realisation of a standard OrnsteinUhlenbeck 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 socalled GaussMarkov 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 SturmLiouville 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 preprint: https://arxiv.org/abs/2210.01658 
19th June 2024 MB0.08 Wilfried KuissiKamdem (AIMS Ghana/University of Rwanda) Pricing and hedging of (pathdependent) claims based on nontradable assets for EpsteinZin utility We present an EpsteinZin utility indifference pricing and hedging for multidimensional tradable and nontradable assets models. We provide an explicit expression for the utility indifference prices and their corresponding derivative hedges. Using forwardbackward SDE method and Malliavin calculus, in a possibly nonMarkovian 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) 

21st June 2024 Joint Session with the Guillmore Centre for Financial Technology WBS Teaching Centre 2:003:30pm Please note that registration is required. Registration 

3rd July 2024 Room MB0.02 Min Dai Equilibrium MeanVariance Strategy with Transaction Costs We study continuoustime meanvariance portfolio selection in the presence of proportional transaction costs, which can be formulated as a timeinconsistent 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 meanvariance criteria with a constant risk preference may yield absurd equilibrium strategies in the presence of transaction costs. We find that a timevarying 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 MeanVariance 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 meanvariance preferences with different riskaversion coefficients. To hedge against the random fluctuations of their individual endowments, the two agents may enter a risksharing 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 freeboundary problem that provides the solution to the agents' optimal equilibrium problem. Furthermore, we derive the explicit solution to this freeboundary 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 (Universität 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 socalled Lipschitz sets which turn out to be a suitable domain for a weaker notion of the generator. This is defined using Gammaconvergence in an appropriate function space. We show that the Gammagenerator 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 socalled Chernoff approximation. The talk is based on joint work with Jonas Blessing, Robert Denk and Max Nendel. 
3rd November  Leandro SanchezBetancourt (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 closedform. 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 largetime analysis. We circumvent this issue by lifting the system to a measurevalued stochastic PDE introduced by Cuchiero and Teichmann, whence we retrieve the Markov property. Leveraging on the associated generalised Feller property, we extend the KrylovBogoliubov theorem to this infinitedimensional 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 quasihyperbolic discounting In this talk, I will introduce a continuoustime portfolio selection problem faced by an agent with Sshaped 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 timeinconsistent version of the problem featuring quasihyperbolic 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

Paolo Guasoni (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 longlived agents with heterogeneous riskaversion and timepreference make consumption and investment decisions, trading risky assets and borrowing from and lending to each other. For small growth fluctuations, we obtain closedform 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 
Adrien Richou (Université 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 nonconvex 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 (University of Warwick) Coupling of multidimensional Lévy 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 Lévy processes attracted to a multidimensional stable law in the smalltime regime. In this talk, the main focus will be on the development of two novel couplings between arbitrary purejump Lévy 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 nonnormal 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  Olivier Menoukeu Pamen (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 EpsteinZin 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 nonMarkovian 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 (University of Warwick) Optimal Stopping with Trees In this talk, we will first review a recent method for solving highdimensional optimal stopping problems using deep Neural Networks. Second, we propose an alternative algorithm replacing Neural Networks by CARTtrees 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 maxcall benchmark example. We also show how our algorithm can be used to plot stopping boundaries. 
15th March 2023 /cancelled/ /will be rescheduled/ 
Daniel Schwarz (University College London) Radner equilibrium and systems of quadratic BSDEs with discontinuous generators We establish the existence of a Radner Equilibrium in an incomplete, continuoustime 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

Eyal Neuman (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 Volterratype propagator along with temporary price impact. We formulate these problems as minimization of a revenuerisk 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 revenuerisk 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 nonparametric 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

Max Nendel (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 infinitedimensional 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 
Umut Cetin (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="" wellknown="" presence="" of="" killing="" introduces="" loss="" accuracy..="" we="" introduce="" driftimplicit="" euler="" method="" to="" bring="" convergence="" rate="" back="" optimal="" can="" be="" obtained="" in="" absence="" killing,="" using="" theory="" recurrent="" transformations="" developed="" recently.="" although="" current="" setup="" assumes="" onedimensional="" setting,="" multidimensional="" extension="" within="" reach="" as="" soon="" systematic="" treatment="" available="" higher="" dimensions.<="" p=""> </u]]> 
21st June 2023 Room MS.03 
Tolulope Fadina (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 worstcase, 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 ValueatRisk, a relevant issue for risk management practice. 
14th July 2023 (On Friday) Room MS.03 
Samuel Cohen (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 lowdimensional approximation, with hopefully small error. In this talk we will see how, in the case where the underlying process is a finitestate Markov Chain, results on the stability of filters can be strengthened to show that this introduces a wellcontrolled error, leveraging tools from information geometry. (Based on joint work with Eliana Fausti) 
15th Oct 2021  Nazem Khan (University of Warwick) Sensitivity to large losses and arbitrage for convex risk measuresLink opens in a new window 
Thu 4th Nov 2021, 2pm (online only) 
Matteo Burzoni (Università 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 MuhleKarbe (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 (University of Warwick) 
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 (University of Warwick) Convexity Corrections via a Markovfunctional approachLink opens in a new window 
Wed 15th June 2022 3pm in MS.04 
Cosimo Andrea Munari (University of Zurich) 
16 Oct 2020  Ruodu WangLink opens in a new window (University of Waterloo) 
An axiomatic foundation for the Expected ShortfallLink opens in a new window  
23 Oct 2020  Moris StrubLink opens in a new window (Southern University of Science and TechnologyLink opens in a new window) 
Forward RankDependent Performance Criteria: TimeConsistent Investment Under Probability Distortion 

30 Oct 2020  Jorge Gonzalez CazaresLink opens in a new window (Warwick) 
Monte Carlo methods for the extrema of Levy models  
13 Nov 2020  Daniel Lacker (Columbia University) 
Local stochastic volatility models and inverting the Markovian projection  
20 Nov 2020  Xiaofei ShiLink opens in a new window (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  JeanFrancois ChassagneuxLink opens in a new window (Université de Paris) 
Modeling carbon markets using ForwardBackward SDEs  
2 Feb 2021 (unusual time!)  Yufei Zhang (Oxford University) 
Deep neural network approximations to stochastic control problems  
12 Feb 2021  Said HamadeneLink opens in a new window (Le Mans Université) 
Meanfield reflected backward stochastic differential equations  
19 Feb 2021  Eduardo DavilaLink opens in a new window (Yale University) 
Optimal Financial Transaction Taxes  
26 Feb 2021  Bahman AngoshtariLink opens in a new window (University of Miami) 
Optimal Consumption under a HabitFormation Constraint  
5 Mar 2021  Dylan Possamai (ETH) 
Timeinconsistent control and backward integral Volterra SDEs 
28 April 2021 (34PM)  Erhan Bayraktar (University of Michigan) 
Department Colloquium  
7 May 2021  Masaaki Fukasawa (Osaka University) 
Volatility has to be rough  
14 May 2021  Xun Li (Hong Kong Polytechnic University) 
An Optimal Investment Problem with Nonsmooth and Nonconcave Utility over a Finite Time Horizon  
21 May 2021  Miryana Grigorova (University of Leeds) 
Pricing and hedging of options in nonlinear incomplete financial market modelsLink opens in a new window  
28 May 2021  Giorgio Ferrari (Bielefeld University) 
TWOSIDED SINGULAR CONTROL OF AN INVENTORY WITH UNKNOWN DEMAND TREND  
4 June 2021  Stefan Ankirchner (University of Jena) 
The De VylderGoovaerts 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) 
IdentificationRobust 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 nonlinear 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) 

Optimal trade execution with transient relative price impact and directional views: A variational approach to a 3dimensional nonconvex 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  
12.11.2018  FudanWarwick Workshop on Financial Mathematics and Stochasitc Analysis 
23.11.2018  Alexander Cox (University of Bath) 
Utility Maximisation with ModelIndependent Trading Constraints  
30.11.2018  Sigrid Källblad (Vienna University of Technology) 
Stochastic control of measurevalued martingales with applications to robust pricing and Skorokhod embedding problems 
18.01.2019  Alex Mijatovic (University of Warwick) 
Stability of overshoots of zero mean random walks  
25.01.2019  Michael Tehranchi (University of Cambridge) 
A BlackScholes inequality: Applications and generalisations 

01.02.2019  Neofytos Rodosthenous (Queen Mary University of London) 
Optimal timing for governmental control of the debttoGDP ratio  
15.02.2019  Matija Vidmar (University of Ljubljana) 
On a family of nonlinear optimal martingale transport problems 

22.02.2019  Mihail Zervos (LSE) 
Risksharing with twosided limited commitment: a duality approach in continuous time 

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) 
Meanfield 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 

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 

cancelled  
01.12.2017  Samuel Cohen (Oxford) 
Uncertainty in KalmanBucy Filtering  
08.12.2017  Yiqing Lin (École Polytechnique) 
Secondorder 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  Sören Christensen (Hamburg) 
NonSmooth Verification for Impulse Control Problems  
16.03.2018  Dörte 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 HighFrequency Trading with Imperfect Competition  
11.05.2018  Thaleia Zariphopoulou (Austin) 
Meanfield and nagent 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) 
Modelfree Valuation of Barrier Options  
29.06.2018  Cosimo AndreaMunari (Zürich) 
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 Cayé (ETH Zürich) 
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) 
EpsteinZin Stochastic Differential Utility  
05.05.2017  Paolo Guasoni (Dublin City) 
Leveraged Funds: Robust Replication and Performance Evaluation  
19.05.2017  Luciano Campi (LSE) 
Nplayer 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) 
Superhedging with proportional transaction costs under uncertainty : a randomization approach  
23.06.2017  Johannes MuhleKarbe (Michigan) 
A RiskNeutral Equilibrium Leading to Uncertain Volatility Pricing 