Stochastic Minimum Principle for Partially Observed Systems Subject to Continuous and Jump Diffusion Processes and Driven by Relaxed Controls

TL;DR

This paper develops a stochastic minimum principle for partially observed control systems influenced by both continuous and jump diffusion processes, considering relaxed controls, and establishes existence and necessary conditions for optimal controls.

Contribution

It introduces a stochastic minimum principle for non-convex control problems with relaxed controls, covering both diffusion and jump processes, and proves existence and optimality conditions.

Findings

Existence of optimal relaxed controls for the considered systems.

Necessary conditions of optimality derived for systems with diffusion and jump processes.

Framework applicable to non-convex stochastic control problems with partial observations.

Abstract

In this paper we consider non convex control problems of stochastic differential equations driven by relaxed controls. We present existence of optimal controls and then develop necessary conditions of optimality. We cover both continuous diffusion and Jump processes.