Risk-sensitive discounted cost criterion for Continuous-time Markov decision processes on a general state space

TL;DR

This paper studies risk-sensitive control for continuous-time jump Markov processes with unbounded rates, establishing existence and uniqueness of solutions to the HJB equation and optimal controls under Lyapunov conditions.

Contribution

It extends risk-sensitive control theory to general state spaces with unbounded rates, providing existence and uniqueness results for the HJB equation and optimal controls.

Findings

Proved existence and uniqueness of HJB solutions.

Established existence of optimal Markov controls.

Handled unbounded transition and cost rates.

Abstract

In this paper, we consider risk-sensitive discounted control problem for continuous-time jump Markov processes taking values in general state space. The transition rates of underlying continuous-time jump Markov processes and the cost rates are allowed to be unbounded. Under certain Lyapunov condition, we establish the existence and uniqueness of the solution to the Hamilton-Jacobi-Bellman (HJB) equation. Also we prove the existence of optimal risk-sensitive control in the class of Markov control.