Weak Closed-Loop Solvability of Stochastic Linear Quadratic Optimal Control Problems of Markovian Regime Switching System

TL;DR

This paper explores the conditions under which stochastic linear quadratic control problems with Markovian regime switching are solvable in open-loop and weak closed-loop forms, establishing their equivalence and providing a method for finding optimal strategies.

Contribution

It introduces an alternative characterization of open-loop solvability and proves the equivalence with weak closed-loop solvability for Markovian regime switching systems.

Findings

Open-loop and weak closed-loop solvabilities are equivalent.

Perturbation approach characterizes open-loop solvability.

Method demonstrated through an illustrative example.

Abstract

In this paper, we investigate the open-loop and weak closed-loop solvabilities of stochastic linear quadratic (LQ, for short) optimal control problem of Markovian regime switching system. Interestingly, these two solvabilities are equivalent. We first provide an alternative characterization of the open-loop solvability of the LQ problem using the perturbation approach. Then, we study the weak closed-loop solvability of the LQ problem of Markovian regime switching system, and establish the equivalent relationship between open-loop and weak closed-loop solvabilities. Finally, we present an example to illustrate the procedure for finding weak closed-loop optimal strategies within the framework of Markovian regime switching system.