Central Moments and Risk-Sensitive Optimality in Markov Reward Processes

0583660 - ÚTIA 2024 RIV CZ eng C - Konferenční příspěvek (zahraniční konf.)
Sladký, Karel
Central Moments and Risk-Sensitive Optimality in Markov Reward Processes.
Praha: Czech University of Life Sciences Prague, 2021. ISBN 978-80-213-3126-6. In: MME 2021, 39th International Conference on Mathematical Methods in Economics. Conference Proceedings. Prague: Faculty of Economics and Management, Czech University of Life Sciences Prague, 2021 - (Hlavatý, R.), s. 446-451. ISBN 978-80-213-3126-6.
[MME 2021: International Conference on Mathematical Methods in Economics /39./. Prague (CZ), 08.09.2021-10.09.2021]
Grant CEP: GA ČR GA18-02739S
Institucionální podpora: RVO:67985556
Klíčová slova: discrete- and continuous-time Markov reward chains * exponential utility * moment generating functions
Obor OECD: Statistics and probability
http://library.utia.cas.cz/separaty/2024/E/sladky-0583660.pdf

In this note we consider discrete- and continuous-time Markov decision processes with finite state space. There is no doubt that usual optimality criteria examined in the literature on optimization of Markov reward processes, e.g. total discounted or mean reward, may be quite insufficient to select more sophisticated criteria that reflect also the variability-risk features of the problem. In this note we focus on models where the stream of rewards generated by the Markov process 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 non-zero, 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 it higher moments are taken into account. Using Taylor expansion of the utility function we present explicit formulas for calculating variance a higher central moments of the total reward generated by the |Markov reward process along with its asymptotic behaviour.
Trvalý link: https://hdl.handle.net/11104/0352094