scholarly journals Restricted Coherent Risk Measures and Actuarial Solvency

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Christos E. Kountzakis
Keyword(s):  
Minimization Problem ◽  
Risk Measures ◽  
Insurance Company ◽  
Coherent Risk Measures ◽  
Dual Representation ◽  
Coherent Risk ◽  
Representation Form ◽  
Solvency Capital

We prove a general dual representation form for restricted coherent risk measures, and we apply it to a minimization problem of the required solvency capital for an insurance company.

scholarly journals On the dual representation of coherent risk measures

2017 ◽  
Vol 262 (1) ◽  
pp. 29-46 ◽  
Author(s):  
Marcus Ang ◽  
Jie Sun ◽  
Qiang Yao
Keyword(s):  
Risk Measures ◽  
Coherent Risk Measures ◽  
Dual Representation ◽  
Coherent Risk

scholarly journals Minimizing spectral risk measures applied to Markov decision processes

2021 ◽  
Author(s):  
Nicole Bäuerle ◽  
Alexander Glauner
Keyword(s):  
Minimization Problem ◽  
Risk Measures ◽  
Risk Measure ◽  
Sufficient Conditions ◽  
Planning Horizon ◽  
Insurance Company ◽  
Existence Of A Solution ◽  
Discounted Cost ◽  
Spectral Risk Measures ◽  
Markov Decision

AbstractWe 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.

scholarly journals Rearrangement Invariant, Coherent Risk Measures on L<sup>0</sup>

2015 ◽  
Vol 04 (01) ◽  
pp. 22-25
Author(s):  
Christos E. Kountzakis ◽  
Dimitrios G. Konstantinides
Keyword(s):  
Risk Measures ◽  
Coherent Risk Measures ◽  
Coherent Risk
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