The Maximum Principle for Discounted Optimal Control of Partially Observed Forward-Backward Stochastic Systems with Jumps on Infinite Horizon

TL;DR

This paper develops a maximum principle for optimal control of partially observed stochastic systems with jumps on an infinite horizon, providing new solvability results and comparison analyses.

Contribution

It introduces a novel maximum principle for infinite horizon partially observed systems with jumps, including solvability and ergodic analysis.

Findings

Established unique solvability of infinite horizon stochastic differential equations with jumps.

Derived an ergodic maximum principle for the control problem.

Compared different types of infinite horizon stochastic systems and their optimal controls.

Abstract

This paper is concerned with a discounted optimal control problem of partially observed forward-backward stochastic systems with jumps on infinite horizon. The control domain is convex and a kind of infinite horizon observation equation is introduced. The uniquely solvability of infinite horizon forward (backward) stochastic differential equation with jumps is obtained and more extended analysis, especially for the backward case, is made. Some new estimates are first given and proved for the critical variational inequality. Then an ergodic maximum principle is obtained by introducing some infinite horizon adjoint equations whose uniquely solvabilities are guaranteed necessarily. Finally, some comparison are made with two kinds of representative infinite horizon stochastic systems and their related optimal controls.