Pontryagin`s approach to the risk-sensitive control problem for fractional backward stochastic differential equations

Abstract

This paper investigates a class of optimal control problems for backward stochastic systems driven by fractional Brownian motion with Hurst parameter varying between 0 and 1, and the cost functional is risk-sensitive. Using variational inequality techniques, we derive optimality conditions under the assumption of a convex set of admissible controls. We first address the risk-neutral case to establish existence of an optimal solution. The framework extends classical control theory to fractional backward stochastic systems. A linear–quadratic stochastic example is provided to illustrate the applicability of the results.