Stochastic maximum principle for system governed by forward backward stochastic differential equation with risk sensitive control problem and application

Abstract

Throughout this thesis, we focused our aim on the problem of optimal control under a risk-sensitive performance functional, where the systems studied are given by a backward stochastic differential equation, fully coupled forward-backward stochastic differential equation, and fully coupled forward backward stochastic differential equation with jump. As a preliminary step, we use the risk neutral which is an extension of the initial control system where the set of admissible controls are convex in all the control problems, and an optimal solution exists. Then, we study the necessary as well as sufficient optimality conditions for risk sensitive performance, we illustrate our main results by giving applied examples of risk sensitive control problem. The first is under linear stochastic dynamics with exponential quadratic cost function. The second example deals with an optimal portfolio choice problem in financial market specially the model of control cash flow of a firm or project. The last one is an example of mean-variance for risk sensitive control problem applied in cash flow market.