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

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