Robust utility maximization for diffusion market model with misspecified coefficients

TL;DR

This paper addresses the problem of maximizing utility of terminal wealth in a diffusion market model with uncertain parameters, providing explicit solutions via HJBI equations.

Contribution

It introduces a robust utility maximization framework for diffusion markets with misspecified coefficients and derives explicit solutions using HJBI equations.

Findings

Explicit characterization of the robust utility maximization solution.

Solution expressed through HJBI equation.

Applicable to markets with uncertain trend and volatility.

Abstract

The paper studies the robust maximization of utility of terminal wealth in the diffusion financial market model. The underlying model consists with risky tradable asset, whose price is described by diffusion process with misspecified trend and volatility coefficients, and non-tradable asset with a known parameter. The robust utility functional is defined in terms of a HARA utility function. We give explicit characterization of the solution of the problem by means of a solution of the HJBI equation.