Mean-Variance Hedging and Forward-Backward Stochastic Differential Filtering Equations

This paper is concerned with a mean-variance hedging problem with partial information, where the initial endowment of an agent may be a decision and the contingent claim is a random variable. This problem is explicitly solved by studying a linear-quadratic optimal control problem with non-Markov control systems and partial information. Then, we use the result as well as filtering to solve some examples in stochastic control and finance. Also, we establishbackwardandforward-backwardstochastic differential filtering equations which aredifferentfrom the classical filtering theory introduced by Liptser and Shiryayev (1977), Xiong (2008), and so forth.