Copula-Based Risk Aggregation and the Significance of Reinsurance

Alexandra Dias, Isaudin Ismail and Aihua Zhang ()
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Alexandra Dias: School for Business and Society, University of York, York YO10 5ZF, UK
Isaudin Ismail: Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Pagoh 84600, Johor, Malaysia
Aihua Zhang: Department of Mathematical Sciences, College of Science, Mathematics and Technology, Wenzhou-Kean University, 88 Daxue Road, Ouhai, Wenzhou 325060, China

Risks, 2025, vol. 13, issue 3, 1-23

Abstract: Insurance companies need to calculate solvency capital requirements in order to ensure that they can meet their future obligations to policyholders and beneficiaries. The solvency capital requirement is a risk management tool essential for addressing extreme catastrophic events that result in a high number of possibly interdependent claims. This paper studies the problem of aggregating the risks coming from several insurance business lines and analyses the effect of reinsurance on the level of risk. Our starting point is to use a hierarchical risk aggregation method which was initially based on two-dimensional elliptical copulas. We then propose the use of copulas from the Archimedean family and a mixture of different copulas. Our results show that a mixture of copulas can provide a better fit to the data than an individual copula and consequently avoid over- or underestimation of the capital requirement of an insurance company. We also investigate the significance of reinsurance in reducing the insurance company’s business risk and its effect on diversification. The results show that reinsurance does not always reduce the level of risk, but can also reduce the effect of diversification for insurance companies with multiple business lines.

Keywords: copula; reinsurance; capital requirement; risk aggregation; value at risk; tail value at risk (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2025
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