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On the Diversification Effect in Solvency II for Extremely Dependent Risks

Chen, Yongzhao, Cheung, Ka Chun, Yam, Sheung Chi Phillip, Yuen, Fei Lung, Zeng, Jia (2023) On the Diversification Effect in Solvency II for Extremely Dependent Risks. Risks, 11 (8). Article Number 143. ISSN 2227-9091. (doi:10.3390/risks11080143) (KAR id:102463)


In this article, we investigate the validity of diversification effect under extreme-value copulas, when the marginal risks of the portfolio are identically distributed, which can be any one having a finite endpoint or belonging to one of the three maximum domains of attraction. We show that Value-at-Risk (V@R) under extreme-value copulas is asymptotically subadditive for marginal risks with finite mean, while it is asymptotically superadditive for risks with infinite mean. Our major findings enrich and supplement the context of the second fundamental theorem of quantitative risk management in existing literature, which states that V@R of a portfolio is typically non-subadditive for non-elliptically distributed risk vectors. In particular, we now pin down when the V@R is super or subadditive depending on the heaviness of the marginal tail risk. According to our results, one can take advantages from the diversification effect for marginal risks with finite mean. This justifies the standard formula for calculating the capital requirement under Solvency II in which imperfect correlations are used for various risk exposures.

Item Type: Article
DOI/Identification number: 10.3390/risks11080143
Uncontrolled keywords: Strategy and Management, Economics, Econometrics and Finance (miscellaneous), Accounting
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
SWORD Depositor: JISC Publications Router
Depositing User: JISC Publications Router
Date Deposited: 16 Aug 2023 13:57 UTC
Last Modified: 09 Jan 2024 10:20 UTC
Resource URI: (The current URI for this page, for reference purposes)

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