A risk-sensitive stochastic maximum principle for fully coupled forward-backward stochastic differential equations with applications

In this paper, we are interested in the problem of optimal control where the system is given by a fully coupled forward-backward stochastic differential equation with a risk-sensitive performance functional. As a preliminary step, we use the risk neutral which is an extension of the initial control system where the admissible controls are convex, and an optimal solution exists.Then, we study the necessary as well as sufficient optimality conditions for risk sensitive performance. At the end of this work, we illustrate our main result by giving an example that deals with an optimal portfolio choice problem in financial market, specifically the model of control cash flow of a firm or project where, for instance, we can set the model of pricing and managing an insurance contract.