Author’s Reply: Application of Coherent Risk Measures to Capital Requirements in Insurance - Discussion by Elias S.W. Shiu

2000 ◽  
Vol 4 (1) ◽  
pp. 116-116
Author(s):  
Philippe Artzner
Keyword(s):  
Risk Measures ◽  
Capital Requirements ◽  
Coherent Risk Measures ◽  
Coherent Risk

RISK MEASURES DERIVED FROM A REGULATOR’S PERSPECTIVE ON THE REGULATORY CAPITAL REQUIREMENTS FOR INSURERS

2020 ◽  
Vol 50 (3) ◽  
pp. 1065-1092
Author(s):  
Jun Cai ◽  
Tiantian Mao
Keyword(s):  
Value At Risk ◽  
Risk Measures ◽  
Wasserstein Distance ◽  
Capital Requirements ◽  
Translation Invariance ◽  
Coherent Risk Measures ◽  
Regulatory Capital ◽  
Coherent Risk ◽  
Positive Homogeneity ◽  
Stop Loss

AbstractIn this study, we propose new risk measures from a regulator’s perspective on the regulatory capital requirements. The proposed risk measures possess many desired properties, including monotonicity, translation-invariance, positive homogeneity, subadditivity, nonnegative loading, and stop-loss order preserving. The new risk measures not only generalize the existing, well-known risk measures in the literature, including the Dutch, tail value-at-risk (TVaR), and expectile measures, but also provide new approaches to generate feasible and practical coherent risk measures. As examples of the new risk measures, TVaR-type generalized expectiles are investigated in detail. In particular, we present the dual and Kusuoka representations of the TVaR-type generalized expectiles and discuss their robustness with respect to the Wasserstein distance.

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 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
Sign in / Sign up

Export Citation Format

Share Document