# On risk-sensitive piecewise deterministic Markov decision processes

## TL;DR

This paper studies risk-sensitive control in piecewise deterministic Markov decision processes, establishing optimality equations, value iteration, and existence of optimal policies, improving results for continuous-time risk-sensitive decision models.

## Contribution

It introduces a framework for risk-sensitive control in PDMDPs, proving optimality equations and policy existence under natural conditions, with significant improvements over prior results.

## Key findings

- Established the optimality equation for the model.
- Justified the value iteration algorithm.
- Proved existence of deterministic stationary optimal policies.

## Abstract

We consider a piecewise deterministic Markov decision process, where the expected exponential utility of total (nonnegative) cost is to be minimized. The cost rate, transition rate and post-jump distributions are under control. The state space is Borel, and the transition and cost rates are locally integrable along the drift. Under natural conditions, we establish the optimality equation, justify the value iteration algorithm, and show the existence of a deterministic stationary optimal policy. Applied to special cases, the obtained results already significantly improve some existing results in the literature on finite horizon and infinite horizon discounted risk-sensitive continuous-time Markov decision processes.