Séminaire commun MATHRISK INRIA / LPSM :
Title : How much should we care what others know? Jump signals in
optimal investment under relative performance concerns
investment problems where investors receive idiosyncratic signals about
impending price shocks and interact through relative performance
concerns. We use Meyer-sigma-fields to introduce signal-driven
strategies and describe investor behavior in both a multi-agent and a
mean-field game setting. Existence of equilibria in both cases is proven
under suitable conditions on the investors’ types, including the
frequency and realiability of their signal processes. Numerical
experiments allow us to investigate properties of these equilibria from
a financial-economic perspective and help us answer the question how
much investors care about what is known by their peers. This is joint
work with Gemma Sedrakjan.
Olivier Guéant (Université Paris 1 Panthéon-Sorbonne)
Title: Market-Making Models: Overview and Applications to Precious Metals Markets
Abstract: Since the foundational work of Ho and Stoll, later refined by Avellaneda and Stoikov, algorithmic market-making models have advanced to include more realistic features, such as trade sizes, complex price dynamics, tiering, externalization, and market impact. These models have been applied to many OTC markets ranging from illiquid corporate bonds to highly liquid foreign exchange markets and cryptocurrencies (price-aware AMMs). This talk will review key developments in the field, highlighting both theoretical advancements and practical applications. It will also introduce a recent extension of these models to address challenges faced by precious metals dealers, who act as market makers in spot markets while hedging with futures. The mathematical framework leverages tools from stochastic optimal control, optimization, variational calculus, and stochastic filtering.
Abstract:
We propose a single-level numerical approach to solve Stackelberg mean field game (MFG) problems. In Stackelberg MFG, an infinite population of agents play a non-cooperative game and choose their controls to optimize their individual objectives while interacting with the principal and other agents through the population distribution. The principal can influence the mean field Nash equilibrium at the population level through policies, and she optimizes her own objective, which depends on the population distribution. This leads to a bi-level problem between the principal and mean field of agents that cannot be solved using traditional methods for MFGs. We propose a reformulation of this problem as a single-level mean field optimal control problem through a penalization approach, and we prove convergence of the reformulated problem to the original problem. We propose a machine learning method based on (feed-forward and recurrent) neural networks and illustrate it with several examples from the literature. Joint work with Gokce Dayanikli, based on: https://arxiv.org/abs/2302.10440
MATHRISK WEEKLY SEMINAR
STOCHASTIC METHODS AND FINANCE
ENPC – INRIA – UGE
RECENT PAST EVENTS
09h – 09:45 : Gudmund PAMMER , ETH Zurich
09:45 – 10:30 : Mehdi TALBI, LPSM
***** 10:30-11h : Pause café *****
11h00 – 11:45 : Robert DENKERT , HU Berlin
11:45 – 12:30: Aurélien ALFONSI, MathRisk CERMICS/ENPC
CONFERENCE UDINE – 14- 16 June 2023
The project-team MATHRISK of INRIA Paris/Ecole des Ponts Paris Tech/ Université Gustave Eiffel, and the Department of Economics and Statistics of the University of Udine are pleased to announce the MathRisk Conference on Numerical Methods in Finance to celebrate the 25th anniversary of the project and the numerical platform PREMIA http://premia.fr
The conference will be held in Udine, on 14 – 16 June 2023 and hosted by the Department of Economics and Statistics of the University of Udine (Italy).
The main topics are: Neural networks and machine learning in computational finance, Stochastic volatility and jumps models, Risk measures, Systemic risk, stochastic control, (Martingale) Optimal transport, Mean-field systems and games, Green finance, Quantum computing in finance.
Plenary Lectures: Christa Cuchiero (Vienna University), Antoine Jacquier (Imperial College London), Arnulf Jentzen (University of Münster & The Chinese University of Hong Kong, Shenzhen), Peter Tankov (ENSAE Paris).
Invited finance industry speakers: Michel Crouhy (Natixis), Christophe Michel (CA-CIB)
Deadlines: Abstract submission: 15 March 2023, Notification of acceptance: 15 April 2023, Registration (free but mandatory): 15 May 2023.
Conference Web Site : https://mathrisk2023.sciencesconf.org/
