Finite horizon risk-sensitive continuous-time Markov decision processes with unbounded transition and cost rates

TL;DR

This paper establishes the existence of optimal policies and solutions for finite horizon risk-sensitive continuous-time Markov decision processes with unbounded transition and cost rates, extending theoretical understanding in this area.

Contribution

It proves the existence and uniqueness of solutions to the optimality equation under unbounded conditions, and justifies the Feynman-Kac formula for such processes.

Findings

Existence of optimal policies under unbounded rates

Uniqueness of solutions to the optimality equation

Validation of the Feynman-Kac formula for these processes

Abstract

We consider a risk-sensitive continuous-time Markov decision process over a finite time duration. Under the conditions that can be satisfied by unbounded transition and cost rates, we show the existence of an optimal policy, and the existence and uniqueness of the solution to the optimality equation out of a class of possibly unbounded functions, to which the Feynman-Kac formula was also justified to hold.