Closed-Loop Solvability of Stochastic Linear-Quadratic Optimal Control Problems with Poisson Jumps

TL;DR

This paper investigates the optimal control of stochastic systems with Poisson jumps, introducing closed-loop strategies characterized by Riccati integral-differential equations and backward stochastic differential equations.

Contribution

It extends stochastic LQ control theory to include Poisson jumps and indefinite coefficients, providing a new characterization of optimal strategies.

Findings

Characterization of optimal strategies via Riccati integral-differential equations

Introduction of closed-loop strategies for systems with Poisson jumps

Handling indefinite coefficients in stochastic LQ problems

Abstract

This paper is concerned with the stochastic linear-quadratic optimal control problem with Poisson jumps. The coefficients in the state equation and the weighting matrices in the cost functional are all deterministic but are allowed indefinite. The notion of closed-loop strategies is introduced, and the optimal closed-loop strategy is characterized by a Riccati integral-differential equation and a backward stochastic differential equation with Poisson jumps.