  This paper analyzes the stability of optimal policies in the long-run
stochastic control framework with an averaged risk-sensitive criterion for
discrete-time MDPs on finite state-action space. In particular, we study the
robustness of optimal controls when perturbations to the risk-aversion
parameter are applied, and investigate the Blackwell property, together with
its link to the risk-sensitive vanishing discount approximation framework.
Finally, we present examples that help to better understand the intricacies of
the risk-sensitive control framework.
