Central Moments and Risk-Sensitive Optimality in Markov Reward Chains

0490663 - ÚTIA 2019 SK eng C - Konferenční příspěvek (zahraniční konf.)
Sladký, Karel
Central Moments and Risk-Sensitive Optimality in Markov Reward Chains.
Quantitative Methods in Economics: Multiple Criteria Decision Making XIX. Bratislava: University of Economics, Bratislava, 2018 - (Reiff, M.; Gežík, P.), s. 325-331. ISBN 978-80-89962-07-5.
[Quantitative Methods in Economics: Multiple Criteria Decision Making XIX. Trenčianské Teplice (SK), 23.05.2018-25.05.2018]
Grant CEP: GA ČR GA18-02739S
Institucionální podpora: RVO:67985556
Klíčová slova: Discrete-time Markov reward chains * exponential utility * moment generating functions * formulae for central moments
Obor OECD: Applied Economics, Econometrics
http://library.utia.cas.cz/separaty/2018/E/sladky-0490663.pdf

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.
Trvalý link: http://hdl.handle.net/11104/0286786