Mean-Variance Hedging Under Partial Information

Abstract

We consider the mean-variance hedging 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 the initial mean-variance hedging problem is equivalent to a new mean-variance hedging problem with an additional correction term, which is formulated in terms of observable processes. We prove that the value process of the reduced problem is a square trinomial with coefficients satisfying a triangle system of backward stochastic differential equations and the filtered wealth process of the optimal hedging strategy is characterized as a solution of a linear forward equation.