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

Jun Cai and Tiantian Mao

ASTIN Bulletin, 2020, vol. 50, issue 3, 1065-1092

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.

Date: 2020
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