A game theoretical approach to homothetic robust forward investment performance processes in stochastic factor models

TL;DR

This paper introduces a novel game-theoretic framework for modeling homothetic robust forward investment performance in markets influenced by stochastic factors, linking it with ergodic BSDEs and risk-sensitive games.

Contribution

It develops a new representation of robust forward performance processes using zero-sum stochastic differential games and ergodic BSDEs, connecting to classical utility models.

Findings

Representation of homothetic robust forward performance processes in factor form

Connection established between stochastic differential games and classical utility models

Application demonstrated for robust investment processes with negative realizations

Abstract

This paper studies an optimal forward investment problem in an incomplete market with model uncertainty, in which the underlying stocks depend 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 homothetic robust forward performance processes 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 robust expected utilities for long time horizons. Finally, we give an example to illustrate that our approach can be applied to address a type of robust forward investment performance processes with negative realization processes.