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Extreme Value Theory and Copulas: Reinsurance in the Presence of Dependent Risks

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  • Queensley C Chukwudum

    (PAUSTI - Pan African University Institute of Basic Sciences, Technology and Innovation)

Abstract

An insurer's ability to accurately estimate the accumulation of risk, particularly in the right hand tail, is vital in ensuring that his risk appetites matches his risk exposures. This paper, therefore, focuses on the modeling of the extremal dependence structure between insurance risks using the Generalized Pareto distribution and the copula technique. The results obtained after comparing the dependence between large losses from two lines of business (motor and fire) of the Nigerian insurance industry and two specific non-life insurance companies, indicates that the correlation coefficients vary and is generally weak. With the aid of the archimedean copula, the analysis makes use of the data pair exhibiting the highest correlation to draw particular attention to the importance of taking into account the extremal dependence structure when quantifying the risk capital, allocating risk and when estimating the net reinsurance premium under different reinsurance strategies.

Suggested Citation

  • Queensley C Chukwudum, 2018. "Extreme Value Theory and Copulas: Reinsurance in the Presence of Dependent Risks," Working Papers hal-01855971, HAL.
    • Handle: RePEc:hal:wpaper:hal-01855971
    Note: View the original document on HAL open archive server: https://hal.science/hal-01855971v1
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    1. repec:cup:astinb:v:26:y:1996:i:02:p:201-212_00 is not listed on IDEAS
    2. Debbie Dupuis & Bruce Jones, 2006. "Multivariate Extreme Value Theory And Its Usefulness In Understanding Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(4), pages 1-27.
    3. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    4. Constantinescu, Corina & Hashorva, Enkelejd & Ji, Lanpeng, 2011. "Archimedean copulas in finite and infinite dimensions—with application to ruin problems," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 487-495.
    5. Rocco Roberto Cerchiara & Francesco Acri, 2016. "Aggregate Loss Distribution And Dependence: Composite Models, Copula Functions And Fast Fourier Transform For The Danish Re Insurance Data," Working Papers 201608, Università della Calabria, Dipartimento di Economia, Statistica e Finanza "Giovanni Anania" - DESF.
    6. Martin Eling & Denis Toplek, 2009. "Risk and return of reinsurance contracts under copula models," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 751-775.
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