Risk Measures Derived From a Regulator’s Perspective on the Regulatory Capital Requirements for Insurers

39 Pages Posted: 22 Feb 2018

See all articles by Jun Cai

Jun Cai

University of Waterloo - Department of Statistics and Actuarial Science

Tiantian Mao

University of Science and Technology of China (USTC) - Department of Statistics and Finance

Date Written: September 21, 2017

Abstract

In this paper, we propose new risk measures from a regulator's perspective on the regulatory capital requirements for insurers. 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, TVaR, and expectile measures but also provide new approaches to generate feasible and practical coherent risk measures. We also present the Dual and Kusuoka representations of the TVaR-type generalized expectiles, and discuss their robustness with respect to the Wasserstein distance. The empirical study on stock portfolio selections shows that the new risk measures perform better than the classical TVaR when stocks have large volatilities.

Keywords: Dutch Risk Measure, TVaR, Expectile, Coherent Risk Measure, Stop-Loss Reinsurance, Kuosuoka Representation, Portfolio Selection

Suggested Citation

Cai, Jun and Mao, Tiantian, Risk Measures Derived From a Regulator’s Perspective on the Regulatory Capital Requirements for Insurers (September 21, 2017). Available at SSRN: https://ssrn.com/abstract=3127285 or http://dx.doi.org/10.2139/ssrn.3127285

Jun Cai

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

Tiantian Mao (Contact Author)

University of Science and Technology of China (USTC) - Department of Statistics and Finance ( email )

96, Jinzhai Road
Hefei, Anhui 230026
China

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