Risk-Sensitivity and Average Optimality in Markov and Semi-Markov Reward Processes

0536246 - ÚTIA 2021 RIV CZ eng K - Conference Paper (Czech conference)
Sladký, Karel
Risk-Sensitivity and Average Optimality in Markov and Semi-Markov Reward Processes.
Proceedings of the 38th International Conference on Mathematical Methods in Economics. Brno: Faculty of Business Economics, Mendel University, 2020 - (Kapounek, S.; Vránová, H.), s. 537-543. ISBN 978-80-7509-734-7.
[INTERNATIONAL CONFERENCE ON MATHEMATICAL METHODS IN ECONOMICS (MME 2020) /38./. Brno (CZ), 09.09.2020-11.09.2020]
R&D Projects: GA ČR GA18-02739S
Institutional support: RVO:67985556
Keywords : Markov and semi-Markov reward processes * exponential utility function * risk sensitivity
OECD category: Applied Economics, Econometrics
http://library.utia.cas.cz/separaty/2020/E/sladky-0536246.pdf

This contribution is devoted to risk-sensitivity in long-run average optimality of Markov and semi-Markov reward processes. Since the traditional average optimality criteria cannot reflect the variability-risk features of the problem, we are interested in more sophisticated approaches where the stream of rewards generated by the Markov chain that is evaluated by an exponential utility function with a given risk sensitivity coefficient. Recall that for the risk sensitivity coefficient equal to zero (i.e. the so called risk-neutral case) we arrive at traditional optimality criteria, if the risk sensitivity coefficient is close to zero the Taylor expansion enables to evaluate variability of the generated total reward. Observe that the first moment of the total reward corresponds to expectation of total reward and the second central moment to the reward variance. In this note we present necessary and sufficient risk-sensitivity and risk-neutral optimality conditions for long run risk-sensitive average optimality criterion of unichain Markov and semi-Markov reward processes.
Permanent Link: http://hdl.handle.net/11104/0314173