Mean Field Portfolio Games with Epstein-Zin Preferences

Paper: arXiv 2505.07231

Authors: Guanxing Fu, Ulrich Horst

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.

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical contribution to stochastic control and mean field games using advanced mathematical tools like quadratic BSDEs and stochastic maximum principles. However, it is purely theoretical and completely lacks empirical backtesting, real-world data application, or code implementation.

Research Flowchart

  flowchart TD
    A[Goal: Study Mean Field Portfolio Games with Epstein-Zin Preferences] --> B[Inputs: Non-Markovian Framework & Deterministic Setting]
    B --> C[Apply Stochastic Maximum Principle & Nonlinear Transformation]
    C --> D[Solve Coupled Forward-Backward Stochastic Differential Equations]
    D --> E[Outcome 1: Prove 1-to-1 Correspondence Between Nash Equilibria & BSDE Solutions]
    D --> F[Outcome 2: Derive Explicit Closed-Form Investment & Consumption Policies]