Risk-sensitive optimal control of hidden Markov models: structural results

The authors consider a risk-sensitive optimal control problem for (finite state and action spaces) hidden Markov models (HMM). They present results of an investigation on the nature and structure of risk-sensitive controllers for HMM. Several general structural results are presented, as well as a particular case study of a popular benchmark problem. For the latter, they obtain structural results for the optimal risk-sensitive controller and compare it to that of the risk-neutral controller. Furthermore, they show that indeed the risk-sensitive controller and its corresponding information state converge to the known solutions for the risk-neutral situation as the risk factor goes to zero. They also study the infinite and general risk aversion cases.