Optimal consumption and investment under relative performance criteria with Epstein-Zin utility

Jodi Dianetti, Frank Riedel, Lorenzo Stanca

Published 2024-02-12, updated 2024-03-20Version 2

We consider the strategic interaction of traders in a continuous-time financial market with Epstein-Zin-type recursive intertemporal preferences and performance concerns. We derive explicitly an equilibrium for the finite player and the mean-field version of the game, based on a study of geometric backward stochastic differential equations of Bernoulli type that describe the best replies of traders. Our results show that Epstein-Zin preferences can lead to substantially different equilibrium behavior.