Central Moments and Risk-Sensitive Optimality in Markov Reward Processes

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Central Moments and Risk-Sensitive Optimality in Markov Reward Processes

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Central Moments and Risk-Sensitive Optimality in Markov Reward Processes

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA18-02739S" target="_blank" >GA18-02739S: Stochastická optimalizace v ekonomických procesech</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

MME 2021, 39th International Conference on Mathematical Methods in Economics. Conference Proceedings

ISBN

978-80-213-3126-6

ISSN

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e-ISSN

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Počet stran výsledku

6

Strana od-do

446-451

Název nakladatele

Faculty of Economics and Management, Czech University of Life Sciences Prague

Místo vydání

Prague

Místo konání akce

Prague

Datum konání akce

8. 9. 2021

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

000936369700074