Linear-quadratic partially observed forward-backward stochastic differential games and its application in finance

This paper is concerned with a partially observed linear-quadratic game problem driven by forward-backward stochastic differential equations where the forward diffusion coefficients do not contain control variables and the control domains are not necessarily convex. The drift term of the observation equation is linear with respect to the state, and there is correlated noise between the state and the observation equation. By virtue of the classical spike variational method and the backward separation technique, we derive a necessary and a sufficient condition of the stochastic differential game problem. Then we obtain filtering equations and present a feedback representation form of the equilibrium point through Riccati equations. As a practical application, we solve a partial information investment problem involving g-expectation as a convex risk measurement and give the numerical simulation to show the explicit investment strategy and illustrate some reasonable phenomena influenced by common financial parameters.