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Risk Measures Derived From A Regulator’S Perspective On The Regulatory Capital Requirements For Insurers

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  • Cai, Jun
  • Mao, Tiantian

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.

Suggested Citation

  • Cai, Jun & Mao, Tiantian, 2020. "Risk Measures Derived From A Regulator’S Perspective On The Regulatory Capital Requirements For Insurers," ASTIN Bulletin, Cambridge University Press, vol. 50(3), pages 1065-1092, September.
    • Handle: RePEc:cup:astinb:v:50:y:2020:i:3:p:1065-1092_13
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    Cited by:

    1. Mao, Tiantian & Stupfler, Gilles & Yang, Fan, 2023. "Asymptotic properties of generalized shortfall risk measures for heavy-tailed risks," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 173-192.
    2. Samuel Solgon Santos & Marcelo Brutti Righi & Eduardo de Oliveira Horta, 2022. "The limitations of comonotonic additive risk measures: a literature review," Papers 2212.13864, arXiv.org, revised Jan 2024.

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