Mean Field Games for Optimal Investment Under Relative Performance Criteria

TL;DR

This paper applies the Mean Field Game framework to a portfolio optimization problem involving agents competing based on both absolute and relative wealth, deriving explicit strategies for CRRA and CARA utilities.

Contribution

It extends the Mean Field Game approach to include both CRRA and CARA utility cases in a competitive investment setting.

Findings

Explicit optimal strategies for CRRA utility.

Explicit optimal strategies for CARA utility.

Demonstrates tractability of the mean field approach in competitive investment models.

Abstract

In this paper, we study the portfolio optimization problem formulated by Lacker and Soret. They formulate a finite time horizon model that allows agents to be competitive, measuring their utility not only by their absolute wealth but also relative performance compared to the average of other agents. While the finite population or $n$-player game is tractable in some cases, the authors present the Mean Field Game framework to solve this problem. Here, we seek to use this framework to clearly detail the optimal investment and consumption strategies in the CRRA utility case as was briefly outlined in Lacker and Soret, but also derive a solution in the CARA utility case.