Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar by Ludovic Tangpi: “Optimal Investment in a Large Population of Competitive and Heterogeneous Agents”

Speaker:

Ludovic Tangpi, Princeton University

Title:

Optimal Investment in a Large Population of Competitive and Heterogeneous Agents

Abstract:

We consider a large crowd of exponential utility maximizers acting competitively in the sense that each agent is concerned with the relative performance of their peers. In contrast to the growing literature on the question, we allow agents to weigh the performance of each of their peers differently. This leads to a game among heterogeneous agents set on a graph. We show that if the underlying graph stems from a step graphon then the finite population game converges to a so-called graphon game whose well-posedness is studied. This is a game played by a continuum of interacting players generalizing the mean field game (which corresponds to the constant graphon case). The analysis is based on purely probabilistic arguments, allows for trading constraints and a “not so dense graph”. The talk is based on a joint work with Louise Zhou.

 

Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar