A Game Theoretical Approach to Homothetic Robust Forward Investment Performance Processes in Stochastic Factor Models

Abstract

This paper studies an optimal forward investment problem in an incomplete market with model uncertainty, in which the dynamics of the underlying stocks depends on the correlated stochastic factors. The uncertainty stems from the probability measure chosen by an investor to evaluate the performance. We obtain directly the representation of the power robust forward performance process in factor-form by combining the zero-sum stochastic differential game and ergodic BSDE approach. We also establish the connections with the risk-sensitive zero-sum stochastic differential games over an infinite horizon with ergodic payoff criteria, as well as with the classical power robust expected utility for long time horizons.

Keywords: Forward Performance Process; Model Uncertainty; Self-Generating Stochastic Differential Game; Ergodic BSDE; Ergodic Risk-Sensitive Stochastic Differential Game

JEL Classification: G11