Long-run risk sensitive impulse control

Abstract: In this paper we consider long-run risk sensitive average cost impulse control applied to a continuous-time Feller-Markov process. Using the probabilistic approach, we show how to get a solution to a suitable continuous-time Bellman equation and link it with the impulse control problem. The optimal strategy for the underlying problem is constructed as a limit of dyadic impulse strategies by exploiting regularity properties of the linked risk sensitive optimal stopping value functions. In particular, this shows that the discretized setting could be used to approximate near optimal strategies for the underlying continuous time control problem, which facilitates the usage of the standard approximation tools. For completeness, we present examples of processes that could be embedded into our framework.