| Contents |
| We study a linear-quadratic optimal control problem derived by forward-backward
stochastic differential equations, where drift coefficient of
observation equation is linear with respect to state, and
observation noise is correlated with state noise, in the sense that the cross-variation of state and observation is nonzero.
A backward separation approach is introduced. Combining it with variational method and stochastic filtering, two optimality
conditions and a feedback representation of optimal control are
derived. Closed-form optimal solutions are obtained in some
particular cases. As an application of the optimality conditions, a
generalized recursive utility problem from financial markets is
solved explicitly. |
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