The Global Maximum Principle for Optimal Control of Partially Observed Stochastic Systems Driven by Fractional Brownian Motion

TL;DR

This paper develops a maximum principle for optimal control of partially observed stochastic systems driven by both Brownian and fractional Brownian motions, introducing new processes to handle the lack of Girsanov transformation.

Contribution

It introduces a novel approach to derive the maximum principle for systems driven by fractional Brownian motion without Girsanov transformation.

Findings

Derived the adjoint backward stochastic differential equations.

Established necessary conditions for optimal control.

Extended maximum principle to fractional Brownian motion systems.

Abstract

In this paper we study the stochastic control problem of partially observed (multi-dimensional) stochastic system driven by both Brownian motions and fractional Brownian motions. In the absence of the powerful tool of Girsanov transformation, we introduce and study new stochastic processes which are used to transform the original problem to a "classical one". The adjoint backward stochastic differential equations and the necessary condition satisfied by the optimal control (maximum principle) are obtained.