G-Expected Utility Maximization with Ambiguous Equicorrelation

Abstract

This paper studies the expected utility maximization problem with respect to a controlled state process with multiple noises, whose pairwise correlations are equal and ambiguous. Using the G-expectation theory, we solve for the robust stochastic controls explicitly from a Hamilton-Jacobi-Bellman-Isaacs equation and deduce a robust choice of the equicorrelation coefficient. We also generalize the results to a block equicorrelation structure, where we strike the balance between efficiency and tractability. Although we face with many ambiguous parameters that may be interactive in the general case, we manage to derive an analytical solution to the robust stochastic controls under the ambiguity of a two-block equicorrelated structure via the solution to a system of polynomial equations. The results have significant implications to the investment and reinsurance problems among many others.