A Revisit to Optimal Control of Forward-Backward Stochastic Differential System with Observation Noise

TL;DR

This paper reexamines the optimal control problem for forward-backward stochastic differential systems with observation noise, providing improved bounds and unified optimality conditions for partial information scenarios.

Contribution

It introduces a unified approach to derive necessary and sufficient optimality conditions and improves control bounds from L^8 to L^4.

Findings

Derived unified optimality conditions for the control problem.

Improved control bounds from L^8 to L^4.

Provided verification theorem for the control system.

Abstract

This paper revisits the partial information optimal control problem considered by Wang, Wu and Xiong [Wang et al 2013], where the system is derived by a controlled forward-backward stochastic differential equation with correlated noises between the system and the observation. For this type of partial information optimal control problem, one necessary and one suffcient (a verification theorem) conditions of optimality are derived using a unified way. We improve the $L^p-$ bounds on the control from $L^8$ in [Want et al 2013] to $L^4$ in this paper.