# zbMATH — the first resource for mathematics

Solution to the risk-sensitive average cost optimality equation in a class of Markov decision processes with finite state space. (English) Zbl 1023.90076
Summary: This work concerns discrete-time Markov decision processes with finite state space and bounded costs per stage. The decision maker ranks random costs via the expectation of the utility function associated to a constant risk sensitivity coefficient, and the performance of a control policy is measured by the corresponding (long-run) risk-sensitive average cost criterion. The main structural restriction on the system is the following communication assumption: For every pair of states $$x$$ and $$y$$, there exists a policy $$\pi$$, possibly depending on $$x$$ and $$y$$, such that when the system evolves under $$\pi$$ starting at $$x$$, the probability of reaching $$y$$ is positive. Within this framework, the paper establishes the existence of solutions to the optimality equation whenever the constant risk sensitivity coefficient does not exceed certain positive value.

##### MSC:
 90C40 Markov and semi-Markov decision processes 93E20 Optimal stochastic control 60J05 Discrete-time Markov processes on general state spaces
Full Text: