Summary: 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 establish backward and forward-backward stochastic differential filtering equations which are different
from the classical filtering theory introduced by R. S. Liptser
and A. N. Shiryayev
[Statistics of random processes. I. General theory. Translated by A. B. Aries. Applications of Mathematics. 5. New York etc.: Springer- Verlag (1977; Zbl 0364.60004
)], J. Xiong
[An introduction to stochastic filtering theory. Oxford Graduate Texts in Mathematics 18. Oxford: Oxford University Press (2008; Zbl 1144.93003
)], and so forth.