Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series

Thu, 13 Oct 2022

16:00 - 17:00
L3

### MF-OMO: An Optimization Formulation of Mean-Field Games

Anran Hu
Abstract

Theory of mean-field games (MFGs) has recently experienced an exponential growth. Existing analytical approaches to find Nash equilibrium (NE) solutions for MFGs are, however, by and large restricted to contractive or monotone settings, or rely on the uniqueness of the NE. We propose a new mathematical paradigm to analyze discrete-time MFGs without any of these restrictions. The key idea is to reformulate the problem of finding NE solutions in MFGs as solving an equivalent optimization problem, called MF-OMO (Mean-Field Occupation Measure Optimization), with bounded variables and trivial convex constraints. It is built on the classical work of reformulating a Markov decision process as a linear program, and by adding the consistency constraint for MFGs in terms of occupation measures, and by exploiting the complementarity structure of the linear program. This equivalence framework enables finding multiple (and possibly all) NE solutions of MFGs by standard algorithms such as projected gradient descent, and with convergence guarantees under appropriate conditions. In particular, analyzing MFGs with linear rewards and with mean-field independent dynamics is reduced to solving a finite number of linear programs, hence solvable in finite time. This optimization reformulation of MFGs can be extended to variants of MFGs such as personalized MFGs.

Thu, 20 Oct 2022 09:30 -
Fri, 21 Oct 2022 15:45
The AHL Lecture Theatre, 3rd Floor, Eagle House

### OMI: Artificial Intelligence and Financial Markets workshop - 20th & 21st October 2022

Further Information

Schedule, titles, abstracts, and bios can be found here.

Thu, 27 Oct 2022

16:00 - 17:00
L3

### Merton's optimal investment problem with jump signals

Laura Körber (Berlin)
Abstract

This talk presents a new framework for Merton’s optimal investment problem which uses the theory of Meyer $\sigma$-fields to allow for signals that possibly warn the investor about impending jumps. With strategies no longer predictable, some care has to be taken to properly define wealth dynamics through stochastic integration. By means of dynamic programming, we solve the problem explicitly for power utilities. In a case study with Gaussian jumps, we find, for instance, that an investor may prefer to disinvest even after a mildly positive signal. Our setting also allows us to investigate whether, given the chance, it is better to improve signal quality or quantity and how much extra value can be generated from either choice.
This talk is based on joint work with Peter Bank.

Thu, 03 Nov 2022

16:00 - 17:00
L3

### Decentralised Finance and Automated Market Making: Optimal Execution and Liquidity Provision

Fayçal Drissi
Abstract

Automated Market Makers (AMMs) are a new prototype of
trading venues which are revolutionising the way market participants
interact. At present, the majority of AMMs are Constant Function
Market Makers (CFMMs) where a deterministic trading function
determines how markets are cleared. A distinctive characteristic of
CFMMs is that execution costs for liquidity takers, and revenue for
liquidity providers, are given by closed-form functions of price,
liquidity, and transaction size. This gives rise to a new class of
trading problems. We focus on Constant Product Market Makers with
Concentrated Liquidity and show how to optimally take and make
liquidity. We use Uniswap v3 data to study price and liquidity
dynamics and to motivate the models.

For liquidity taking, we describe how to optimally trade a large
position in an asset and how to execute statistical arbitrages based
on market signals. For liquidity provision, we show how the wealth
decomposes into a fee and an asset component. Finally, we perform
consecutive runs of in-sample estimation of model parameters and
out-of-sample trading to showcase the performance of the strategies.

Thu, 17 Nov 2022

16:00 - 17:00
L3

### Chao Zhang

Chao Zhang
Abstract

More details to follow.