2024 London Mathematical Finance Seminar Series
Jan-March 2024 @ Imperial
Date: Thursday,
January 18, 2024
Time: 16:00-17:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Jean-Paul Decamps, Université Toulouse Capitole
Title: The War of Attrition under Uncertainty: Theory and robust testable implications
Abstract: We study the war of attrition with symmetric information when players' payoffs depend on a homogeneous linear diffusion. We first show that a player's mixed Markov strategy can be represented by an intensity measure over the state space along with a subset of the state space over which the player concedes with probability 1. We then show that, if players are asymmetric, then, in all mixed-strategy Markov-perfect equilibria, these intensity measures must be discrete, and characterize any such equilibrium through a variational system for the players' value functions. We illustrate these findings by revisiting the standard model of exit in a duopoly under uncertainty and construct a mixed-strategy Markov-perfect equilibrium in which attrition takes place on path despite firms having different liquidation values. We show that firms' stock prices comove negatively over the attrition zone and exhibit patterns documented by technical analysis. Joint work with Fabien Gensbittel and Thomas Mariotti.
Date: Thursday, January 18, 2024
Time: 17:00-18:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Zbigniew Palmowski, Wroclaw University of Science and Technology
Title: Cancellable American options under negative discounting
Abstract: Cancellable American options, also known as game options or Israeli options, are American-style derivatives which give the writer the right to terminate the contract for a fixed penalty. I will talk about perpetual cancellable American put options on an asset whose dynamics follow exponential spectrally negative Lévy process. The price and optimal strategies of the buyer and the writer can be deduced from the solution of a corresponding Dynkin game. The new feature of the model is the negative interest rate which brings in difficulties (the payoff grows exponentially fast in time) and interesting strategies. We employ fully probabilistic arguments to argue the existence of the value and of the optimal strategies and characterise explicitly their form. We also prove smooth fit at boundaries of stopping sets enabling their numerical identification. The talk is based on the joint work with Jan Palczewski.
Date: Thursday,
February 1, 2024
Time:
16:00-17:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Julien Guyon, Ecole des Ponts ParisTech
Title: Fast exact joint S&P 500/VIX smile calibration in discrete and continuous time
Abstract: We introduce a novel discrete-time-continuous-time exact calibration method: we first build an S&P 500/VIX jointly calibrating discrete-time model that is later extended to continuous time by martingale interpolation. The benefit is that both steps can be made much faster than the known methods that directly calibrate a continuous-time model. We propose Newton--Sinkhorn and implied Newton algorithms that are much faster than the Sinkhorn algorithm that (Guyon, Risk, April 2020) used to build the first arbitrage-free model exactly consistent with S&P 500 and VIX market data. Using a (purely forward) Markov functional model, we then quickly build an arbitrage-free continuous-time extension of this discrete-time model. Additionally, new model-free bounds on S&P 500 options emphasize the value of the VIX smile information. Extensive numerical tests are conducted. This is joint work with Florian Bourgey (Bloomberg).
Date: Thursday, February 1, 2024
Time: 17:00-18:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Christian Bayer, Weierstrass Institute
Title: Primal and dual optimal stopping with signatures
Abstract: We propose two signature-based methods to solve the optimal stopping problem - that is, to price American options - in non-Markovian frameworks. Both methods rely on a global approximation result for Lp−functionals on rough path-spaces, using linear functionals of robust, rough path signatures. In the primal formulation, we present a non-Markovian generalization of the famous Longstaff-Schwartz algorithm, using linear functionals of the signature as regression basis. For the dual formulation, we parametrize the space of square-integrable martingales using linear functionals of the signature, and apply a sample average approximation. We prove convergence for both methods and present first numerical examples in non-Markovian and non-semimartingale regimes. (Joint work with Luca Pelizzaru and John Schoenmakers.)
Date: Thursday, February 15, 2024
Time: 16:00-17:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Miryana Grigorova, University of Warwick
Title: Optimal stopping and non-zero-sum games: Bermudan strategies meet non-linear evaluations
Abstract: We address an optimal stopping problem over the set of Bermudan-type stopping strategies (which we understand in a more general sense than the stopping strategies for Bermudan options in finance) and with non-linear operators (non-linear evaluations) assessing the rewards, under general assumptions on the non-linear operators. We provide a characterization of the value family V in terms of a suitably defined non-linear Snell envelope of the pay-off family. We establish a Dynamic Programming Principle. We provide an optimality criterion in terms of a non-linear martingale property of V on a stochastic interval. We investigate the non-linear martingale structure and we show that, under suitable conditions, the first time when the value family coincides with the pay-off family is optimal. The reasoning simplifies in the case where there is a finite number, say n, of pre- described stopping times, where n does not depend on the state of nature. We will also discuss a non-zero-sum non-linear game with Bermudan stopping strategies, for which we show the existence of a Nash equilibrium point, via a recursive procedure. We provide examples of non-linear operators from the stochastic control and mathematical finance literature, which enter our framework. The talk is based on an ongoing joint works with Marie-Claire Quenez (Paris) and Peng Yuan (Warwick).
Date: Thursday, February 15, 2024
Time: 17:00-18:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Nikolas Nüsken, King's College London
Title: Optimal control of diffusions, forward-backward stochastic differential equations, and variational inference.
Abstract: The aim of this talk is to present a few recent ideas at the interface of optimal control and machine learning: The core challenge in computational Bayesian statistics is the approximation of probability measures, and when those are considered on path space, many fruitful connections between variational inference and stochastic optimal control emerge. No prior knowledge of variational inference is required – I will give an introduction and point out connection and equivalences.
Date: Thursday, February 29, 2024
Time: 16:00-17:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Olivier Guéant, Université Paris 1 Panthéon-Sorbonne
Title:
Incorporating Variable Liquidity in Optimal Market Making and
Inventory Management Models: A Comparison of Hawkes Processes and
Markov-Modulated Poisson Processes
Abstract: Since Avellaneda and Stoikov's seminal work, market making models have evolved to incorporate increasingly realistic aspects, such as complex price dynamics, price differentiation, adverse selection, or even parameter ambiguity. However, the dynamics of liquidity have been less frequently addressed. While Hawkes processes are a natural choice for modelling beyond constant request and trade intensities, this talk introduces an alternative approach using Markov-modulated Poisson processes (MMPPs). We will explore the benefits and limitations of MMPPs and Hawkes processes in the context of algorithmic market making and inventory management model development.
Date: Thursday, February 29, 2024
Time: 17:00-18:00
Location:
Imperial College London, Huxley Building, Room 140
Speaker: Lyudmila Grigoryeva, University of St. Gallen
Title: Reservoir kernels and Volterra series
Abstract:
A universal kernel is constructed whose sections approximate any causal and time-invariant filter in the fading memory category with inputs and outputs in a finite-dimensional Euclidean space. This kernel is built using the reservoir functional associated with a state-space representation of the Volterra series expansion available for any analytic fading memory filter. It is hence called the Volterra reservoir kernel. Even though the state-space representation and the corresponding reservoir feature map are defined on an infinite-dimensional tensor algebra space, the kernel map is characterized by explicit recursions that are readily computable for specific data sets when employed in estimation problems using the representer theorem. We showcase the performance of the Volterra reservoir kernel in a popular data science application in relation to bitcoin price prediction.
Date: Thursday, March 14, 2024
Time: 16:00-17:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Aurélien Alfonsi, Ecole des Ponts ParisTech
Title: Nonnegativity preserving convolution kernels. Application to Stochastic Volterra Equations in closed convex domains and their approximation.
Abstract: We define and study convolution kernels that preserve nonnegativity. When the past dynamics of a process is integrated with a convolution kernel like in Stochastic Volterra Equations or in the jump intensity of Hawkes processes, this property allows to get the nonnegativity of the integral. We give characterizations of these kernels and show in particular that completely monotone kernels preserve nonnegativity. We then apply these results to analyze the stochastic invariance of a closed convex set by Stochastic Volterra Equations. We also get a comparison result in dimension one. Last, when the kernel is a positive linear combination of decaying exponential functions, we present a second order approximation scheme for the weak error that stays in the closed convex domain under suitable assumptions. We apply these results to the rough Heston model and give numerical illustrations.
Date: Thursday, March 14, 2024
Time: 17:00-18:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Walter Schachermayer, University of Vienna
Title: Martingale Transports in R^n
Abstract: A remarkable theorem of Backhoff-Beiglboeck-Huesman-Kaellblad shows that between probabilities \mu, \nu on R^n which are in convex order and have finite second moments, there always is a unique martingale transport termed “stretched Brownian motion” from \mu to \nu. This transport enjoys many nice properties. A special subclass - with even nicer properties - are termed “Bass martingales”: R. Bass used a similar construction some forty years ago in the context of the Skorohod embedding problem.
We show a necessary and sufficient condition for a stretched Brownian motion to be a Bass martingale, namely irreducibility of the pair (\mu,\nu). The intuitive content of the notion of irreducibility is that there no non-trivial subset of R^n which is invariant under all martingale transports from \mu to \nu.
In the general case, i.e. without imposing irreducibility, we show that the stretched Brownian motion can be decomposed into a family of Bass martingales. This makes contact with previous work by DeMarch-Touzi and Obloj-Siorpaes, as this decomposition generates the universal paving of R^d into invariant sets.
Date: Wednesday, March 27, 2024
Time: 16:00-17:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Sören Christensen, Christian-Albrechts University Kiel
Title: How to Learn from Data in Stochastic Control Problems - An Approach Based on Statistics
Abstract: While theoretical solutions to many stochastic control problems are well understood, their practicality often suffers from the assumption of known dynamics of the underlying stochastic process, which raises the statistical challenge of developing purely data-driven controls. In this talk, we discuss how stochastic control and statistics can be brought together, which we study for various classical control problems with underlying one- and multi-dimensional diffusions and jump processes. The dilemma between exploration and exploitation plays an essential role in the considerations. We find exact sublinear-order convergence rates for the regret and compare the results numerically with those of deep Q-learning algorithms.
Date: Wednesday, March 27, 2024
Time: 17:00-18:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Peter Tankov, ENSAE
Title: Asset pricing under transition scenario uncertainty and model ambiguity
Abstract: We study asset pricing and optimal investment decisions for an economic agent whose future revenues depend on the realization of a scenario from a given set of possible futures. In the first part of the talk, we assume that future scenario is unknown, but that the possible scenarios have equal probabilities, and the agent deduces scenario information progressively by observing a signal. The problem of valuing an investment is formulated as an American option pricing problem with Bayesian learning. In the second part, we assume that the probabilities of individual prospective scenarios are ambiguous and place ourselves into the smooth model of decision making under ambiguity aversion of Klibanoff et al (2005), framing the optimal investment decision as an optimal stopping problem with learning under ambiguity. We then prove a minimax result allowing to reduce this problem to a series of standard optimal stopping problems. The theory is illustrated with two examples: the problem of optimally selling a stock with ambiguous drift, and the problem of optimal divestment from a coal-fired power plant under transition scenario ambiguity.
