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 Shot Glass systems and partial information.Then, we use the Beauty and Skin Care Products result as well as filtering to solve some examples in stochastic control and finance.
Also, we establish backward and forward-backward stochastic differential filtering equations which are different from the classical filtering theory introduced by Liptser and Shiryayev (1977), Xiong (2008), and so forth.