Mean Field Portfolio Games

TL;DR

This paper analyzes mean field portfolio games with random market parameters, deriving explicit Nash equilibria and asymptotic expansions under weak interaction assumptions, contributing to understanding strategic investment in stochastic environments.

Contribution

It introduces a novel approach using mean field FBSDEs to characterize Nash equilibria in portfolio games with random parameters and provides explicit solutions under certain conditions.

Findings

Explicit Nash equilibrium in closed form when market parameters are deterministic

Asymptotic expansion of equilibrium in powers of the competition parameter

Unique equilibrium characterized by a mean field FBSDE with quadratic growth

Abstract

We study mean field portfolio games with random market parameters, where each player is concerned with not only her own wealth but also relative performance to her competitors. We use the martingale optimality principle approach to characterize the unique Nash equilibrium in terms of a mean field FBSDE with quadratic growth, which is solvable under a weak interaction assumption. Motivated by the weak interaction assumption, we establish an asymptotic expansion result in powers of the competition parameter. When the market parameters do not depend on the Brownian paths, we obtain the Nash equilibrium in closed form.