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Central Moments and Risk-Sensitive Optimality in Markov Reward Chains
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SYSNO ASEP 0490663 Document Type C - Proceedings Paper (int. conf.) R&D Document Type The record was not marked in the RIV Title Central Moments and Risk-Sensitive Optimality in Markov Reward Chains Author(s) Sladký, Karel (UTIA-B) RID Number of authors 1 Source Title Quantitative Methods in Economics: Multiple Criteria Decision Making XIX. - Bratislava : University of Economics, Bratislava, 2018 / Reiff Martin ; Gežík Pavel - ISBN 978-80-89962-07-5 Pages s. 325-331 Number of pages 7 s. Publication form Print - P Action Quantitative Methods in Economics: Multiple Criteria Decision Making XIX Event date 23.05.2018 - 25.05.2018 VEvent location Trenčianské Teplice Country SK - Slovakia Event type EUR Language eng - English Country SK - Slovakia Keywords Discrete-time Markov reward chains ; exponential utility ; moment generating functions ; formulae for central moments Subject RIV BB - Applied Statistics, Operational Research OECD category Applied Economics, Econometrics R&D Projects GA18-02739S GA ČR - Czech Science Foundation (CSF) Institutional support UTIA-B - RVO:67985556 UT WOS 000455265500044 Annotation 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),
Kawai (1987), Mandl (1971), Sladký (2005),(2008),(2013), van Dijk and Sladký (2006), White (1988)).
In 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.Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2019
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