  Throughout this paper, we focused our aim on the problem of optimal control
under a risk-sensitive performance functional, where the system is given by a
fully coupled forward-backward stochastic differential equation with jump. The
risk neutral control system has been used as preliminary step, where the
admissible controls are convex, and the optimal solution exists. The necessary
as well as sufficient optimality conditions for risk-sensitive performance are
proved. At the end of this work, we illustrate our main result by giving an
example of mean-variance for risk sensitive control problem applied in cash
flow market.
