Mean Field Portfolio Games with Epstein-Zin Preferences

TL;DR

This paper analyzes mean field portfolio games with Epstein-Zin preferences, establishing a link between Nash equilibria and BSDE solutions, and providing explicit solutions in deterministic cases.

Contribution

It introduces a novel framework connecting Nash equilibria to BSDEs for Epstein-Zin preferences and derives explicit solutions in deterministic scenarios.

Findings

Uniqueness of Nash equilibria established via BSDE correspondence

Explicit closed-form solutions derived for deterministic cases

Framework encompasses classical utility as a special case

Abstract

We study mean field portfolio games under Epstein-Zin preferences, which naturally encompass the classical time-additive power utility as a special case. In a general non-Markovian framework, we establish a uniqueness result by proving a one-to-one correspondence between Nash equilibria and the solutions to a class of BSDEs. A key ingredient in our approach is a necessary stochastic maximum principle tailored to Epstein-Zin utility and a nonlinear transformation. In the deterministic setting, we further derive an explicit closed-form solution for the equilibrium investment and consumption policies.