Minimizing spectral risk measures applied to Markov decision processes

被引:10
作者
Baeuerle, Nicole [1 ]
Glauner, Alexander [1 ]
机构
[1] Karlsruhe Inst Technol KIT, Dept Math, D-76128 Karlsruhe, Germany
关键词
Risk-sensitive Markov decision process; Spectral risk measure; Dynamic reinsurance; OPTIMAL REINSURANCE; REPRESENTATION;
D O I
10.1007/s00186-021-00746-w
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
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 Bauerle 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.
引用
收藏
页码:35 / 69
页数:35
相关论文
共 35 条
[1]   On the coherence of expected shortfall [J].
Acerbi, C ;
Tasche, D .
JOURNAL OF BANKING & FINANCE, 2002, 26 (07) :1487-1503
[2]  
Albrecher H., 2017, Reinsurance: Actuarial and Statistical Aspects, DOI DOI 10.1002/9781119412540
[3]  
[Anonymous], 2014, Advances in neural information processing systems
[4]  
ARROW KJ, 1963, AM ECON REV, V53, P941
[5]   Optimal risk allocation in reinsurance networks [J].
Baeuerle, Nicole ;
Glauner, Alexander .
INSURANCE MATHEMATICS & ECONOMICS, 2018, 82 :37-47
[6]   More Risk-Sensitive Markov Decision Processes [J].
Baeuerle, Nicole ;
Rieder, Ulrich .
MATHEMATICS OF OPERATIONS RESEARCH, 2014, 39 (01) :105-120
[7]   Markov Decision Processes with Average-Value-at-Risk criteria [J].
Baeuerle, Nicole ;
Ott, Jonathan .
MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2011, 74 (03) :361-379
[8]  
Bäuerle N, 2011, UNIVERSITEXT, P1, DOI 10.1007/978-3-642-18324-9
[9]   Markov decision processes with recursive risk measures [J].
Baeuerle, Nicole ;
Glauner, Alexander .
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2022, 296 (03) :953-966
[10]  
Borch K., 1960, T 16 INT C ACT, VI, P597, DOI DOI 10.1017/S05150361000095572-S2.0-27244457311