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

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.Comment: 27 page

Relative Value Iteration for Stochastic Differential Games

We study zero-sum stochastic differential games with player dynamics governed by a nondegenerate controlled diffusion process. Under the assumption of uniform stability, we establish the existence of a solution to the Isaac's equation for the ergodic game and characterize the optimal stationary strategies. The data is not assumed to be bounded, nor do we assume geometric ergodicity. Thus our results extend previous work in the literature. We also study a relative value iteration scheme that takes the form of a parabolic Isaac's equation. Under the hypothesis of geometric ergodicity we show that the relative value iteration converges to the elliptic Isaac's equation as time goes to infinity. We use these results to establish convergence of the relative value iteration for risk-sensitive control problems under an asymptotic flatness assumption