Version 1
: Received: 9 October 2024 / Approved: 9 October 2024 / Online: 10 October 2024 (10:19:23 CEST)
How to cite:
Dias, A.; Ismail, I.; Zhang, A. Copula-Based Risk Aggregation and the Significance of Reinsurance. Preprints2024, 2024100743. https://doi.org/10.20944/preprints202410.0743.v1
Dias, A.; Ismail, I.; Zhang, A. Copula-Based Risk Aggregation and the Significance of Reinsurance. Preprints 2024, 2024100743. https://doi.org/10.20944/preprints202410.0743.v1
Dias, A.; Ismail, I.; Zhang, A. Copula-Based Risk Aggregation and the Significance of Reinsurance. Preprints2024, 2024100743. https://doi.org/10.20944/preprints202410.0743.v1
APA Style
Dias, A., Ismail, I., & Zhang, A. (2024). Copula-Based Risk Aggregation and the Significance of Reinsurance. Preprints. https://doi.org/10.20944/preprints202410.0743.v1
Chicago/Turabian Style
Dias, A., Isaudin Ismail and Aihua Zhang. 2024 "Copula-Based Risk Aggregation and the Significance of Reinsurance" Preprints. https://doi.org/10.20944/preprints202410.0743.v1
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, when extreme catastrophic events occur, resulting 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 in the level of risk. Our starting point is to use a Hierarchical Risk Aggregation method, which was initially based on 2-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 underestimating 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
Subject
Business, Economics and Management, Finance
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
