Title: On risk-sensitive piecewise deterministic Markov decision processes,
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.