A Maximum Principle for Partially Observed Risk-Sensitive Optimal Control Problem of Mean-Field Fbsde

We study a class of risk-sensitive mean-field type optimal control problems of forward-backward stochastic differential equation (FBSDE) under partial information, where the system contains correlated state and observation noises and the cost functional is based on HARA utility function. Using Girsanov's theorem and classical variational technique, we establish a stochastic maximum principle. The adjoint equation is a mean-field FBSDE. Finally, using the maximum principle derived, we investigate an asset-liability management problem. An explicit candidate optimal strategy is obtained.