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

Published online by Cambridge University Press:  22 July 2020

Jun Cai  and
Tiantian Mao
Jun Cai
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ONN2L 3G1, Canada, E-Mail: jcai@uwaterloo.ca
Tiantian Mao*
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui, China, E-Mail: tmao@ustc.edu.cn
*
E-Mail: tmao@ustc.edu.cn
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Abstract

In 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.

Keywords

Dutch risk measureTVaRexpectilecoherent risk measurestop-loss order preservingstop-loss reinsuranceKuosuoka representationG32B16
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 3 , September 2020 , pp. 1065 - 1092
Copyright
© 2020 by Astin Bulletin. All rights reserved

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