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Mean-variance hedging and forward-backward stochastic differential filtering equations. (English) Zbl 1229.91327
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.
MSC:
91G20Derivative securities
49N10Linear-quadratic optimal control problems
60H30Applications of stochastic analysis