0583660 20250131155210.820240305235959.9 978-80-213-3126-6 000936369700074 Praha Czech University of Life Sciences Prague 2021 6 s. P cav_un_epca*0546142978-80-213-3126-6446-451PragueFaculty of Economics and Management, Czech University of Life Sciences Prague2021HlavatýR. discrete- and continuous-time Markov reward chains exponential utility moment generating functions cav_un_auth*0101196 Sladký Karel UTIA-B Ekonometrie Department of Econometrics E E Department of Econometrics Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2024/E/sladky-0583660.pdf GA18-02739S GA ČR cav_un_auth*0363963 In this note we consider discrete- and continuous-time Markov decision processes with finite state space. There is no doubt that usual optimality criteria examined in the literature on optimization of Markov reward processes, e.g. total discounted or mean reward, may be quite insufficient to select more sophisticated criteria that reflect also the variability-risk features of the problem. In this note we focus on models where the stream of rewards generated by the Markov process 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 non-zero, 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 it higher moments are taken into account. Using Taylor expansion of the utility function we present explicit formulas for calculating variance a higher central moments of the total reward generated by the |Markov reward process along with its asymptotic behaviour. cav_un_auth*0414661 MME 2021: International Conference on Mathematical Methods in Economics /39./ 20210908 20210910 Prague CZ BB 10000 10100 10103 2024 1 PR RVO:67985556 https://hdl.handle.net/11104/0352094 S Proceedings Paper Economics|Mathematics Interdisciplinary Applications|Social Sciences Mathematical Methods 2021 C 2021 Praha Czech University of Life Sciences Prague 978-80-213-3126-6 SCOPUS PUBMED 000936369700074 WOS cav_un_epca*0546142 MME 2021, 39th International Conference on Mathematical Methods in Economics. Conference Proceedings Faculty of Economics and Management, Czech University of Life Sciences Prague 2021 Prague 446 451 978-80-213-3126-6 Hlavatý R. 340