On additivity of tail comonotonic risks

Ka Chun Cheung, Hok Kan Ling, Qihe Tang, Sheung Chi Phillip Yam and Fei Lung Yuen

Scandinavian Actuarial Journal, 2019, vol. 2019, issue 10, 837-866

Abstract: As perceived from daily experience together with numerous empirical studies, the multivariate risks demonstrate a strong coherence in the extremal dependence structure especially over the course of financial turmoil or industrial accidents and outbreaks. Under this motivating paradigm, we show the universal asymptotic additivity under upper tail comonotonicity, as the probability level approaching to 1, for Value-at-Risk and Conditional Tail Expectation for a portfolio of fixed number of risks, in which each marginal risk could be any one having a finite endpoint or belonging to one of the three max domains of attraction. Our obtained results do not require the tail equivalence assumption as needed in the existing literature. This resolves a lasting problem in quantitative risk management and covers most distributions commonly encountered in practice.

Date: 2019
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DOI: 10.1080/03461238.2019.1626762

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