Asymptotics of robust utility maximization

Abstract

For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $\lambda\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading strategy and an asymptotic worst-case model in terms of an ergodic Bellman equation. With these results we propose a duality approach to a "robust large deviations" criterion for optimal long-term investment.Comment: Published in at http://dx.doi.org/10.1214/11-AAP764 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Robust utility maximisation in markets with transaction costs

“…The bracket ·, · denotes scalar product in R 2 . Note that the original setting of [20] cannot be directly transferred to the present one as it involves a family of weak solutions of SDEs which are not necessarily definable on our given stochastic basis.…”

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

“…Therefore, Theorem 22 can be viewed as an optimal investment model, and the constant λ is the optimal long-term growth rate of the expected utility of wealth with model uncertainty. Such asymptotic results on robust utility maximization have been treated in [35] using the duality method and are related to "robust large deviations" criteria to optimal long-term investment, that is, the investor aims to maximize the portfolio's growth rate exceeding some threshold C ∈ R under the worst-case probability…”

“…Risk-sensitive optimal control has been widely applied to optimal investment problems (see, [8,17,18,25] and references therein). The corresponding risk-sensitive stochastic differential games are studied in [5,7,9,35] via PDE approach and in [15] via BSDE approach.…”

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

“…The corresponding risk-sensitive stochastic differential games are studied in [2,3,5,27] via PDE approach and in [9] via BSDE approach. In this paper, we apply directly the ergodic BSDE approach to address the zero-sum risk-sensitive stochastic differential game with ergodic payoff criteria over an infinite horizon.…”