Maximum principles for partially observed mean-field stochastic systems with application to financial engineering

This article is concerned with a partially observed optimal control problem derived by stochastic differential equations. One of novel features is that both the state equation and the cost functional are of mean-field type, which results in the problem time inconsistent in the sense that dynamic programming does not hold. Two maximum principles for optimality are obtained using Girsanov theorem, convex variation and approximation of smooth functions. A cash management model is worked out and is explicitly solved by virtue of the maximum principle and stochastic filtering.