# Risk-sensitive Necessary and Sufficient Optimality Conditions and Financial Applications: Fully Coupled Forward-Backward Stochastic Differential Equations with Jump diffusion

## TL;DR

This paper develops necessary and sufficient optimality conditions for risk-sensitive control problems involving fully coupled forward-backward stochastic differential equations with jumps, with applications to financial models like mean-variance in cash flow markets.

## Contribution

It introduces new optimality conditions for risk-sensitive control in complex stochastic systems with jumps, extending previous work to more realistic financial models.

## Key findings

- Established necessary and sufficient optimality conditions for the control problem.
- Applied the theoretical results to a mean-variance risk-sensitive control example.
- Demonstrated the existence of optimal solutions under convex control constraints.

## Abstract

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.