arxiv:2505.07231

Mean Field Portfolio Games with Epstein-Zin Preferences

Published on May 12

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Abstract

Uniqueness of Nash equilibria in mean field portfolio games with Epstein-Zin preferences is established through a correspondence with BSDE solutions and a tailored stochastic maximum principle.

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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.

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