Long-Run Risk-Sensitive Impulse Control
Damian Jelito, Marcin Pitera, Łukasz Stettner · SIAM Journal on Control and Optimization · 2020
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 the 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.