Mean Field Portfolio Games with Epstein-Zin Preferences

Guanxing Fu and Ulrich Horst
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Guanxing Fu: The Hong Kong Polytechnic University
Ulrich Horst: Humboldt University Berlin

No 540, Rationality and Competition Discussion Paper Series from CRC TRR 190 Rationality and Competition

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.

Keywords: epstein-zin utility; mean field game; stochastic maximum principle (search for similar items in EconPapers)
Date: 2025-07-27
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