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Stochastic Finance @ Warwick Seminars

Unless otherwise specified, the Stochastic Finance seminar takes place on Wednesdays starting at 11:00 am. While the seminars will run in person, there is also the possibility to join via MS Teams. If you wish to be added to the respective Team, please contact the seminar organiser Miryana Grigorova.Link opens in a new window

All are welcome.

The first session in Term 1 in the academic year 2023/2024 is on the 4th of October.

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 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

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 non-Gaussian 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 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

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 (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

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. Co-authors: Patrick Chang and Gabriel Garcia-Arenas.

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 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

Neofytos Rodosthenous (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 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)
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>