A partial information linear-quadratic optimal control problem of backward stochastic differential equation with its applications

In this paper, we investigate a kind of partial information linear-quadratic optimal control problem driven by a backward stochastic differential equation, where the state equation and the cost functional contain diffusion terms. Using maximum principle, we derive the corresponding Hamiltonian system, which is a conditional mean-field forward-backward stochastic differential equation. By the backward separation approach and the filtering technique, we get two Riccati equations, and a backward and a forward optimal filtering equations. Then a feedback form of optimal control is obtained. We also extend the control problem to the case of mean-field backward stochastic differential equation under partial information. A corresponding feedback form of optimal control is also obtained.