0517875 20240103223157.920191213235959.9 6 s. E cav_un_epca*0509647978-80-7394-760-6338-343České BudějoviceUniversity of South Bohemia in České Budějovice, Faculty of Economics2019HoudaM.RemešR. semi-Markov processes with rewards discrete and continuous-time Markov reward chains risk-sensitive optimality average reward and variance over time 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/2019/E/sladky-0517875.pdf cav_un_auth*0363963 GA18-02739S GA ČR Semi-Markov decision processes can be considered as an extension of discrete- and continuous-time Markov reward models. Unfortunately, traditional optimality criteria as long-run average reward per time may be quite insufficient to characterize the problem from the point of a decision maker. To this end it may be preferable if not necessary to select more sophisticated criteria that also reflect variability-risk features of the problem. Perhaps the best known approaches stem from the classical work of Markowitz on mean-variance selection rules, i.e. we optimize the weighted sum of average or total reward and its variance. Such approach has been already studied for very special classes of semi-Markov decision processes, in particular, for Markov decision processes in discrete - and continuous-time setting. In this note these approaches are summarized and possible extensions to the wider class of semi-Markov decision processes is discussed. Attention is mostly restricted to uncontrolled models in which the chain is aperiodic and contains a single class of recurrent states. Considering finite time horizons, explicit formulas for the first and second moments of total reward as well as for the corresponding variance are produced. cav_un_auth*0379399 MME 2019: International Conference on Mathematical Methods in Economics /37./ 20190911 20190913 České Budějovice CZ BB 10000 10100 10103 2020 1 PR RVO:67985556 http://hdl.handle.net/11104/0303159 S 2019 SCOPUS PUBMED WOS cav_un_epca*0509647 Conference Proceedings. 37th International Conference on Mathematical Methods in Economics 2019 978-80-7394-760-6 338 343 České Budějovice University of South Bohemia in České Budějovice, Faculty of Economics 2019 Houda M. 340 340 Remeš R.