guest ::
| Home > Conference materials > Papers > Central Moments and Risk-Sensitive Optimality in Markov Reward Processes |
Original title:
Central Moments and Risk-Sensitive Optimality in Markov Reward Processes
Authors: Sladký, Karel
Document type: Papers
Conference/Event: MME 2021: International Conference on Mathematical Methods in Economics /39./, Prague (CZ), 20210908
Year: 2021
Language: eng
Abstract: 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.
Keywords: discrete- and continuous-time Markov reward chains; exponential utility; moment generating functions
Project no.: GA18-02739S (CEP)
Funding provider: GA ČR
Host item entry: MME 2021, 39th International Conference on Mathematical Methods in Economics. Conference Proceedings, ISBN 978-80-213-3126-6
Institution: Institute of Information Theory and Automation AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: http://library.utia.cas.cz/separaty/2024/E/sladky-0583660.pdf
Original record: https://hdl.handle.net/11104/0352094
Permalink: http://www.nusl.cz/ntk/nusl-542035
The record appears in these collections:
Research > Institutes ASCR > Institute of Information Theory and Automation
Conference materials > Papers
Authors: Sladký, Karel
Document type: Papers
Conference/Event: MME 2021: International Conference on Mathematical Methods in Economics /39./, Prague (CZ), 20210908
Year: 2021
Language: eng
Abstract: 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.
Keywords: discrete- and continuous-time Markov reward chains; exponential utility; moment generating functions
Project no.: GA18-02739S (CEP)
Funding provider: GA ČR
Host item entry: MME 2021, 39th International Conference on Mathematical Methods in Economics. Conference Proceedings, ISBN 978-80-213-3126-6
Institution: Institute of Information Theory and Automation AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: http://library.utia.cas.cz/separaty/2024/E/sladky-0583660.pdf
Original record: https://hdl.handle.net/11104/0352094
Permalink: http://www.nusl.cz/ntk/nusl-542035
The record appears in these collections:
Research > Institutes ASCR > Institute of Information Theory and Automation
Conference materials > Papers
Record created 2024-03-24, last modified 2024-04-15