Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/286738 
Year of Publication: 
2021
Citation: 
[Journal:] Mathematical Methods of Operations Research [ISSN:] 1432-5217 [Volume:] 94 [Issue:] 1 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2021 [Pages:] 35-69
Publisher: 
Springer, Berlin, Heidelberg
Abstract: 
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.
Subjects: 
Risk-sensitive Markov decision process
Spectral risk measure
Dynamic reinsurance
JEL: 
C40
G70
G05
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

Files in This Item:
File
Size





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.