Post-Doctoral Research Visit F/M [Campagne post-doctorants] - Multi-Agent Reinforcement Learning for Mean-Field Games and Systemic Risk

This Postdoctoral Research Fellowship position is proposed by the Mathrisk INRIA  Research team, https://team.inria.fr/mathrisk/en/, which is common with INRIA, the Ecole Nationale des Ponts et Chaussées and the University Gustave Eiffel. 

The  Mathrisk team addresses broad research topics in the area of  mathematical handling of risk, embracing risk measurement and risk management, modeling and optimization in quantitative finance and other related domains where risk control is paramount. 

It also develops a numerical platform for quantitative finance(http://www.premia.fr), supported by a consortium of financial institutions.

Mathematical expertise of the team includes stochastic modeling, stochastic analysis, in particular stochastic (partial) differential equations and various aspects of stochastic control and optimal stopping of these equations, stochastic optimization, dynamic game theory, random graphs, martingale optimal transport and numerical probability. In recent years, systemic risk has emerged as a major focus of research. Unlike traditional risk management approaches that primarily consider risks faced by individual institutions, the emphasis now lies on modeling the intricate interrelationships among institutions and the mechanisms of distress propagation across them. Leveraging a multi-agent reinforcement learning (MARL) approach enables a more detailed examination of systemic risk within financial networks. As evidenced by past crises, effective tools for monitoring stability in large and complex financial systems must accurately account for the diverse interconnections within these systems. In this context, our research proposal builds upon our previous findings on systemic risk using a random graph approach, integrating mean-field games and reinforcement learning strategies. This integration enhances both the depth and precision of our analyses within a dynamic financial network framework.

Academic Partnership : Hamed Amini, Associate Professor, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA, email:  aminil@ufl.edu

Travel expenses are covered within the limits of the scale in force.

Assignments 

The objective of this project is to develop data-driven stochastic network models for quantifying systemic risk in financial systems using Multi-Agent Reinforcement Learning (MARL) techniques and Mean-Field Games (MFGs). While systemic risk analysis has seen a surge in interest post-crisis, existing models often lack the ability to capture the heterogeneity, variety of contagion channels, and dynamics of financial networks. By integrating MARL and MFGs, we aim to address these limitations and derive forward-looking systemic risk measurement tools that can adapt and learn from continuous changes in financial networks. Through this approach, we seek to provide a more accurate and insightful understanding of potential future crises while identifying key factors contributing to systemic risk.

References:

• Amini, Z. Cao, and A. Sulem. Limit theorems for default contagion and systemic risk. Mathematics of Operations Research, forthcoming.
• Amini, Z. Cao, A. Minca, and A. Sulem. Ruin probabilities for risk processes in stochastic networks. arXiv:2302.06668, 2023.
• Amini, Z. Cao, and A. Sulem. The default cascade process in stochastic financial networks. Proc. ACM International Conference on AI in Finance (ICAIF’23), 227–234, 2023.
• Amini, Z. Cao, and A. Sulem. Stochastic Graphon Games with Jumps and Approximate Nash Equilibria. SSRN: 4412999, 2023.
• Amini, Z. Cao and A. Sulem. Graphon Mean-Field Backward Stochastic Differential Equations With Jumps and Associated Dynamic Risk Measures, SSRN: 4162616, 2022.
• Amini, A. Minca, and A. Sulem. A dynamic contagion risk model with recovery features. Mathematics of Operations Research, 47(2):1412–1442, 2022.
• Bayraktar, S. Chakraborty, and R. Wu. Graphon mean field systems. The Annals of Applied Probability, 33(5), pp.3587-3619, 2023.
• Borgs, J. T. Chayes, L. Lovasz, V. T. Sos, and K. Vesztergombi. Convergent sequences of dense graphs i: Subgraph frequencies, metric properties and testing. Advances in Mathematics, 219(6):1801–1851, 2008.
• Borgs, J. T. Chayes, L. Lovasz, V. T. Sos, and K. Vesztergombi. Convergent sequences of dense graphs ii. multiway cuts and statistical physics. Annals of Mathematics, pages 151–219, 2012.
• E. Caines and M. Huang. Graphon mean field games and their equations. SIAM Journal on Control and Optimization, 59(6):4373–4399, 2021.
• Carmona, D. B. Cooney, C. V. Graves, and M. Lauriere. Stochastic graphon games: I. the static case. Mathematics of Operations Research, 47(1):750–778, 2022.
• Carmona, J.-P. Fouque, and L.-H. Sun. Mean field games and systemic risk, http://arxiv.org/abs/1308.2172, 2013.
• Cui and H. Koeppl. Learning graphon mean field games and approximate Nash equilibria. arXiv:2112.01280, 2021.
• Garnier, G.Papanicolaou, and T.W.Yang. Large deviations for a mean field model of systemic risk, SIAM Journal on Financial Mathematics, 4(1):151--184, 2013.
• -M. Lasry and P.-L. Lions. Mean field games. Japanese Journal of Mathematics, 2:229--260, 2007.

Collaboration :
The recruited person will work in collaboration with Agnès Sulem, INRIA Paris, agnes.sulem@inria.fr and Hamed Amini, Associate Professor, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA, email:  aminil@ufl.edu

Main activities :

It is expected that the successful candidate will conduct novel research in the proposed topic and will be able to valorize it by writing articles and presenting the results in workshops and conferences. The postdoctoral fellow will also participate to the scientific life of the team, in particular by attendance to the seminars. He/she might visit Prof. Hamed Amini in University of Florida for collaboration. 

PhD in applied mathematics or Computer sciences.

• Subsidized meals
• Partial reimbursement of public transport costs
• Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
• Possibility of teleworking and flexible organization of working hours (after 12 months of contract)
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities
• Access to vocational training

According to civil service salary scales