Long-Run Risk-Sensitive Impulse Control

Abstract

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