Maximum principle for partially observed risk-sensitive optimal control problems of mean-field type

This paper deals with a class of partially observed risk-sensitive optimal control. By virtue of Girsanov׳s theorem and the standard spike variational technique, we establish the maximum principle for the partially observed control problems. Moreover, the sufficient condition is also obtained for the special case by using some concavity conditions. As an application, a linear-quadratic system is presented to demonstrate our results.