Exponential utility maximization under partial information

Abstract

We consider the exponential utility maximization problem under partial information. The underlying asset price process follows a continuous semimartingale and strategies have to be constructed when only part of the information in the market is available. We show that this problem is equivalent to a new exponential optimization problem which is formulated in terms of observable processes. We prove that the value process of the reduced problem is the unique solution of a backward stochastic differential equation (BSDE) which characterizes the optimal strategy. We examine two particular cases of diffusion market models for which an explicit solution has been provided. Finally, we study the issue of sufficiency of partial information.