Central Moments and Risk-Sensitive Optimality in Continuous-Time Markov Reward Processes

0536251 - ÚTIA 2021 RIV SK eng C - Konferenční příspěvek (zahraniční konf.)
Sladký, Karel
Central Moments and Risk-Sensitive Optimality in Continuous-Time Markov Reward Processes.
QUANTITATIVE METHODS IN ECONOMICS : Multiple Criteria Decision Making XX. Bratislava: University of Economics, 2020 - (Reiff, M.; Gežík, P.), s. 305-311. ISBN 978-80-89962-60-0.
[Quantitative Methods in Economics 2020 (Multiple Criteria Decision Making 2020) /20./. Púchov (SK), 27.05.2020-29.05.2020]
Grant CEP: GA ČR GA18-02739S
Institucionální podpora: RVO:67985556
Klíčová slova: Continuous-time Markov reward chains * exponential utility * formulae for central moments
Obor OECD: Statistics and probability
http://library.utia.cas.cz/separaty/2020/E/sladky-0536251.pdf

In this note we consider continuous-time Markov decision processes with finite state space where the stream of rewards generated by the Markov processes 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 nonzero, 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 its higher moments are taken into account. Using Taylor expansion of the utility function we present explicit formulae for calculating variance and higher central moments of the total reward generated by the Markov reward process along with its asymptotic behavior.
Trvalý link: http://hdl.handle.net/11104/0314254