A note on risk-sensitive control of invariant models

According to Assaf, a dynamic programming problem is called invariant if its transition mechanism depends only on the chosen action. This paper studies properties of risk-sensitive invariant problems with a general state space. The main result establishes the optimality equation for the risk-sensitive average cost criterion without any restrictions on the risk factor. Moreover, a practical algorithm is provided for solving the optimality equation in case of a finite action space.