Artikel
Minimizing spectral risk measures applied to Markov decision processes
We study the minimization of a spectral risk measure of the total discounted cost generated by a Markov Decision Process (MDP) over a finite or infinite planning horizon. The MDP is assumed to have Borel state and action spaces and the cost function may be unbounded above. The optimization problem is split into two minimization problems using an infimum representation for spectral risk measures. We show that the inner minimization problem can be solved as an ordinary MDP on an extended state space and give sufficient conditions under which an optimal policy exists. Regarding the infinite dimensional outer minimization problem, we prove the existence of a solution and derive an algorithm for its numerical approximation. Our results include the findings in Bäuerle and Ott (Math Methods Oper Res 74(3):361–379, 2011) in the special case that the risk measure is Expected Shortfall. As an application, we present a dynamic extension of the classical static optimal reinsurance problem, where an insurance company minimizes its cost of capital.
- Language
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Englisch
- Bibliographic citation
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Journal: Mathematical Methods of Operations Research ; ISSN: 1432-5217 ; Volume: 94 ; Year: 2021 ; Issue: 1 ; Pages: 35-69 ; Berlin, Heidelberg: Springer
- Classification
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Wirtschaft
Econometric and Statistical Methods: Special Topics: General
- Subject
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Risk-sensitive Markov decision process
Spectral risk measure
Dynamic reinsurance
- Event
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Geistige Schöpfung
- (who)
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Bäuerle, Nicole
Glauner, Alexander
- Event
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Veröffentlichung
- (who)
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Springer
- (where)
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Berlin, Heidelberg
- (when)
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2021
- DOI
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doi:10.1007/s00186-021-00746-w
- Last update
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10.03.2025, 11:44 AM CET
Data provider
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Artikel
Associated
- Bäuerle, Nicole
- Glauner, Alexander
- Springer
Time of origin
- 2021
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