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Conference Paper (international conference)

Central Moments and Risk-Sensitive Optimality in Markov Reward Chains

Sladký Karel

: Quantitative Methods in Economics: Multiple Criteria Decision Making XIX, p. 325-331 , Eds: Reiff Martin, Gežík Pavel

: Quantitative Methods in Economics: Multiple Criteria Decision Making XIX, (Trenčianské Teplice, SK, 20180523)

: GA18-02739S, GA ČR

: Discrete-time Markov reward chains, exponential utility, moment generating functions, formulae for central moments

: http://library.utia.cas.cz/separaty/2018/E/sladky-0490663.pdf

(eng): There is no doubt that usual optimization criteria examined in the literature on optimization of Markov reward processes, e.g. total discounted or mean reward, may be quite insufficient to characterize the problem from the point of the decision maker. To this end it is necessary to select more sophisticated criteria that reflect also the variability-risk features of the problem (cf. Cavazos-Cadena and Fernandez-Gaucherand (1999), Cavazos-Cadena and Hernández-Hernández (2005), Howard and Matheson (1972), Jaquette (1976), \nKawai (1987), Mandl (1971), Sladký (2005),(2008),(2013), van Dijk and Sladký (2006), White (1988)). \nIn the present paper we consider unichain Markov reward processes with finite state spaces and assume that the generated reward is evaluated by an exponential utility function. Using the Taylor expansion we present explicit formulae for calculating variance and higher central moments of the total reward generated by the Markov reward chain along with its asymptotic behavior and the growth rates if the considered time horizon tends to infinity.

: BB

: 50202

2019-01-07 08:39