Risk-sensitive and Mean Variance Optimality in Continuous-time Markov Decision Chains

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

Risk-sensitive and Mean Variance Optimality in Continuous-time Markov Decision Chains

Popis výsledku v původním jazyce

In this note we consider continuous-time Markov decision processes with finite state and actions spaces where the stream of rewards generated by the Markov processes is evaluated by an exponential utility function with a given risk sensitivitycoefficient (so-called risk-sensitive models). If the risk sensitivity coefficient equals zero (risk-neutral case) we arrive at a standard Markov decision process. Then we can easily obtain necessary and sufficient mean reward optimality conditions and the variability can be evaluated by the mean variance of total expected rewards. For the risk-sensitive case, i.e. if the risk-sensitivity coefficient is non-zero, for a given value of the risk-sensitivity coefficient we establish necessary and sufficient optimality conditions for maximal (or minimal) growth rate of expectation of the exponential utility function, along with mean value of the corresponding certainty equivalent. Recall that in this case along with the total reward also its higher moments are taken into account.

Název v anglickém jazyce

Risk-sensitive and Mean Variance Optimality in Continuous-time Markov Decision Chains

Popis výsledku anglicky

In this note we consider continuous-time Markov decision processes with finite state and actions spaces where the stream of rewards generated by the Markov processes is evaluated by an exponential utility function with a given risk sensitivitycoefficient (so-called risk-sensitive models). If the risk sensitivity coefficient equals zero (risk-neutral case) we arrive at a standard Markov decision process. Then we can easily obtain necessary and sufficient mean reward optimality conditions and the variability can be evaluated by the mean variance of total expected rewards. For the risk-sensitive case, i.e. if the risk-sensitivity coefficient is non-zero, for a given value of the risk-sensitivity coefficient we establish necessary and sufficient optimality conditions for maximal (or minimal) growth rate of expectation of the exponential utility function, along with mean value of the corresponding certainty equivalent. Recall that in this case along with the total reward also its higher moments are taken into account.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

50201 - Economic Theory

Projekt

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

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název statě ve sborníku

36th International Conference Mathematical Methods in Economics

ISBN

978-80-7378-371-6

ISSN

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e-ISSN

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Počet stran výsledku

6

Strana od-do

497-512

Název nakladatele

MatfyzPress

Místo vydání

Praha

Místo konání akce

Jindřichův Hradec

Datum konání akce

12. 9. 2018

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

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