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Métodos Matemáticos em Finanças

A soft introduction to mean-field games and similar models
Roberto Machado Velho

Instituto Nacional de Matematica Pura e Aplicada
Segunda-feira, 2 de setembro de 2019, 17:00
Sala 232


Mean-field games (MFG) is a recent area that emerged both from mathematical and engineering fields. Its ideas come from statistical mechanics and its application range from city planning to economics, to finance. The main idea is to provide an approximation for the description of a system with many particles/agents/players evolving in time while in equilibrium under a non-collaborative differential game.
The ingredients are (stochastic) optimal control and Fokker-Planck equations. Surprisingly, many PDEs can be regarded as a kind of MFG. The goal of this talk is to introduce the notions to formulate a mean-field game problem, describe modeling through some examples, and connect it with other mathematical problems. We will focus on the ideas of the construction rather than technicalities.
Time allowing, we discuss numerical methods and the relation to multi-agent reinforcement learning problems