Constrained stochastic LQ control on infinite time horizon with regime switching

TL;DR

This paper develops a novel approach to solve infinite horizon stochastic LQ control problems with regime switching and cone constraints, by introducing extended Riccati equations and deriving explicit optimal controls.

Contribution

It introduces two new extended stochastic Riccati equations for infinite horizon problems with regime switching and constraints, providing explicit solutions and applications.

Findings

Existence of nonnegative solutions to ESREs proved.

Explicit optimal control and value derived.

Application to portfolio optimization with regime switching.

Abstract

This paper is concerned with a stochastic linear-quadratic (LQ) optimal control problem on infinite time horizon, with regime switching, random coefficients, and cone control constraint. To tackle the problem, two new extended stochastic Riccati equations (ESREs) on infinite time horizon are introduced. The existence of the nonnegative solutions, in both standard and singular cases, is proved through a sequence of ESREs on finite time horizon. Based on this result and some approximation techniques, we obtain the optimal state feedback control and optimal value for the stochastic LQ problem explicitly. Finally, we apply these results to solve a lifetime portfolio selection problem of tracking a given wealth level with regime switching and portfolio constraint.