Forward utilities and Mean-field games under relative performance concerns

TL;DR

This paper develops a mean-field game framework for portfolio management with forward utilities of CARA type, addressing relative performance concerns and deriving equilibrium strategies in both finite and infinite agent settings.

Contribution

It introduces a novel application of forward utilities in mean-field games for portfolio optimization under relative performance, including solutions for finite and infinite agent models.

Findings

Derived equilibrium strategies for single stock and asset specialization scenarios.

Analyzed best response dynamics and equilibrium conditions.

Discussed time-consistent model selection in sequential horizons.

Abstract

We introduce the concept of mean field games for agents using Forward utilities of CARA type to study a family of portfolio management problems under relative performance concerns. Under asset specialization of the fund managers, we solve the forward-utility finite player game and the forward-utility mean-field game. We study best response and equilibrium strategies in the single common stock asset and the asset specialization with common noise. As an application, we draw on the core features of the forward utility paradigm and discuss a problem of time-consistent mean-field dynamic model selection in sequential time-horizons.