Risk-sensitive finite-horizon piecewise deterministic Markov decision processes

This paper deals with risk-sensitive piecewise deterministic Markov decision processes, where the expected exponential utility of a finite horizon reward is to be maximized. Both the transition rates and reward functions are allowed to be unbounded. Feynman-Kac's formula is developed in our setup, using which along with an approximation technique, we establish the associated Hamilton-Jacobi-Bellman equation and the existence of risk-sensitive optimal policies under suitable conditions. (C) 2019 Elsevier B.V. All rights reserved.