Maximum Principle of Forward-Backward Stochastic Differential System of Mean-Field Type with Observation Noise

TL;DR

This paper develops maximum principle conditions for optimal control of mean-field forward-backward stochastic systems with partial observation and correlated noises, extending stochastic control theory to more complex, realistic models.

Contribution

It establishes necessary and sufficient Pontryagin maximum principles for mean-field systems with partial observation and correlated noises, a novel extension in stochastic control theory.

Findings

Derived unified maximum principle conditions for optimal control.

Addressed systems with observation-dependent coefficients and correlated noises.

Provided theoretical framework for partial information control problems.

Abstract

This paper is concerned with the partial information optimal control problem of mean-field type under partial observation, where the system is given by a controlled mean-field forward-backward stochastic differential equation with correlated noises between the system and the observation, moreover the observation coefficients may depend not only on the control process and but also on its probability distribution. Under standard assumptions on the coefficients, necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin's maximum principles are established in a unified way.