A Partially Observed Optimal Control Problem for Mean-Field Type Forward-Backward Stochastic System

This paper studies an optimal control problem derived by mean-field type forward-backward stochastic system, whose novel features are as follows: (i) Both the state equation and the cost functional are of mean-field type; (ii) The observation depends on the control; (iii) The drift coefficient of the observation equation is linear with respect to the state x. These features result in intrinsic difficulties in solving the control problem. Using a backward separation method with a decomposition technique, these difficulties are overcome and a maximum principle for optimality is derived. An asset-liability management model with recursive utility is worked out and is explicitly solved by the maximum principle and the filtering of forward-backward stochastic system.