Discounted approximations in risk-sensitive average Markov cost chains with finite state space

This work concerns with Markov chains on a finite state space. It is supposed that a state-dependent cost is associated with each transition, and that the evolution of the system is watched by an agent with positive and constant risk-sensitivity. For a general transition matrix, the problem of approximating the risk-sensitive average criterion in terms of the risk-sensitive discounted index is studied. It is proved that, as the discount factor...