SIAM Journal on Control and Optimization, Vol.47, No.5, 2381-2409, 2008
MEAN-VARIANCE HEDGING UNDER PARTIAL INFORMATION
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.
Keywords:backward stochastic differential equation;semimartingale market model;incomplete markets;mean-variance hedging;partial information