Department of Pattern Recognition

(eng): In this note we consider continuous-time Markov decision processes with finite state space where the stream of rewards generated by the Markov processes is evaluated by an exponential utility function with a given risk sensitivity coefficient (so-called risk-sensitive models). For the risk-sensitive case, i.e. if the considered risk-sensitivity coefficient is nonzero, we establish explicit formulas for growth rate of expectation of the exponential utility function. Recall that in this case along with the total reward also its higher moments are taken into account. Using Taylor expansion of the utility function we present explicit formulae for calculating variance and higher central moments of the total reward generated by the Markov reward process along with its asymptotic behavior.