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Risk aggregation in Solvency II through recursive log-normals

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  • Bølviken, Erik
  • Guillen, Montserrat

Abstract

It is argued that the accuracy of risk aggregation in Solvency II can be improved by updating skewness recursively. A simple scheme based on the log-normal distribution is developed and shown to be superior to the standard formula and to adjustments of the Cornish–Fisher type. The method handles tail-dependence if a simple Monte Carlo step is included. A hierarchical Clayton copula is constructed and used to confirm the accuracy of the log-normal approximation and to demonstrate the importance of including tail-dependence. Arguably a log-normal scheme makes the logic in Solvency II consistent, but many other distributions might be used as vehicle, a topic that may deserve further study.

Suggested Citation

  • Bølviken, Erik & Guillen, Montserrat, 2017. "Risk aggregation in Solvency II through recursive log-normals," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 20-26.
    • Handle: RePEc:eee:insuma:v:73:y:2017:i:c:p:20-26
    DOI: 10.1016/j.insmatheco.2016.12.006
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    References listed on IDEAS

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    1. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    2. Alexander Braun & Hato Schmeiser & Florian Schreiber, 2015. "Solvency II's Market Risk Standard Formula: How Credible Is the Proclaimed Ruin Probability," Journal of Insurance Issues, Western Risk and Insurance Association, vol. 38(1), pages 1-30.
    3. Eling, Martin, 2012. "Fitting insurance claims to skewed distributions: Are the skew-normal and skew-student good models?," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 239-248.
    4. Bermúdez, Lluís & Ferri, Antoni & Guillén, Montserrat, 2013. "A Correlation Sensitivity Analysis Of Non-Life Underwriting Risk In Solvency Capital Requirement Estimation," ASTIN Bulletin, Cambridge University Press, vol. 43(1), pages 21-37, January.
    5. Filipović, Damir, 2009. "Multi-Level Risk Aggregation," ASTIN Bulletin, Cambridge University Press, vol. 39(2), pages 565-575, November.
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    Cited by:

    1. Eling, Martin & Jung, Kwangmin, 2020. "Risk aggregation in non-life insurance: Standard models vs. internal models," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 183-198.
    2. Eric Beutner & Henryk Zähle, 2018. "Bootstrapping Average Value at Risk of Single and Collective Risks," Risks, MDPI, vol. 6(3), pages 1-30, September.
    3. Lina M Cortés & Juan F. Rendón & Javier Perote, 2021. "Determining the banking solvency risk in times of COVID-19 through Gram-Charlier expansions," Documentos de Trabajo de Valor Público 19593, Universidad EAFIT.

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    More about this item

    Keywords

    Clayton copula; Cornish–Fisher; Moment matching; Recursive skewness; Standard formula; Sum of log-normals;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation

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