Robust Utility Maximization in a Stochastic Factor Model

Abstract

We give an explicit PDE characterization for the solution of a robust utilitymaximization problem in an incomplete market model, whose volatility, interest rateprocess, and long-term trend are driven by an external stochastic factor process. Therobust utility functional is defined in terms of a HARA utility function with negativerisk aversion and a dynamically consistent coherent risk measure, which allows for modeluncertainty in the distributions of both the asset price dynamics and the factor process.Our method combines two recent advances in the theory of optimal investments: thegeneral duality theory for robust utility maximization and the stochastic control approach to the dual problem of determining optimal martingale measures.