Risk-sensitive optimal control of hidden Markov models: a case study

We consider a risk-sensitive optimal control problem for hidden Markov models (HMM), i.e., controlled Markov chains where state information is only available to the controller via an output (message) process. The optimal control of HMM under standard, risk-neutral performance criteria, e.g., discounted and average costs, has received much attention in the past. By reference to a 2-state replacement problem with failure-prone units, it is discussed how risk-sensitivity manifests itself in a controller