Risk-Sensitive Average Optimality in Markov Decision Chains

Abstract

We consider a Markov decision chain X = {X _n, n = 0, 1, ...} with finite state space $\mathcal{I}$ = {1, 2, ...,N} and a finite set $\mathcal{A}_i$ = {1, 2, ...,K _i} of possible decisions (actions) in state i ∈ $\mathcal{I}$. Supposing that in state i ∈ $\mathcal{I}$ action k ∈ $\mathcal{A}_i$ is selected, then state j is reached in the next transition with a given probability p ^k_ij and one-stage transition reward r _ij will be accrued to such transition.