Risk-sensitive Markov control processes (Q2873849)

The authors propose a generalized definition of convex risk measures (CRMs) to include the measures considered in behavioral economics and they apply a constructive approach which maintains the Markov property assuring existence of stationary optimal policies for two infinite-horizon objectives, namely discounted total risk and average risk. The definition is extended onto Markovian temporal structures called risk maps which are discussed in the Markov control processes context by adding control parameters. The two types of infinite-horizon objectives are optimized via dynamic programming techniques. The results are compared with classical Markov control processes and with entropic maps. As an example, the authors discuss a one-dimensional simple linear model with mean-semideviation and prove that the proposed sufficient conditions for average risk are satisfied. The paper is difficult to read and the practical implications of the presented results are not clear.