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Modeling and Management of Nonlinear Dependencies–Copulas in Dynamic Financial Analysis

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  • Martin Eling
  • Denis Toplek

Abstract

We study the influence of nonlinear dependencies on a non‐life insurer's risk and return profile. To achieve this, we integrate several copula models in a dynamic financial analysis framework and conduct numerical tests. We also test risk management strategies in response to adverse outcomes. Nonlinear dependencies have a crucial influence on the insurer's risk profile that can hardly be affected by the analyzed management strategies. We find large differences in risk assessment for the ruin probability and for the expected policyholder deficit. This has important implications for insurers, regulators, and rating agencies that use these measures as a foundation for internal risk models, capital standards, and ratings.

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  • Martin Eling & Denis Toplek, 2009. "Modeling and Management of Nonlinear Dependencies–Copulas in Dynamic Financial Analysis," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 651-681, September.
    • Handle: RePEc:bla:jrinsu:v:76:y:2009:i:3:p:651-681
    DOI: 10.1111/j.1539-6975.2009.01318.x
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    2. Mejdoub, Hanène & Ben Arab, Mounira, 2018. "Impact of dependence modeling of non-life insurance risks on capital requirement: D-Vine Copula approach," Research in International Business and Finance, Elsevier, vol. 45(C), pages 208-218.
    3. Dorothea Diers & Martin Eling & Christian Kraus & Andreas Reuß, 2012. "Market-consistent embedded value in non-life insurance: how to measure it and why," Journal of Risk Finance, Emerald Group Publishing, vol. 13(4), pages 320-346, August.
    4. Gatzert, Nadine & Kellner, Ralf, 2011. "The influence of non-linear dependencies on the basis risk of industry loss warranties," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 132-144, July.
    5. Christoph Werner & Tim Bedford & John Quigley, 2018. "Sequential Refined Partitioning for Probabilistic Dependence Assessment," Risk Analysis, John Wiley & Sons, vol. 38(12), pages 2683-2702, December.
    6. Benjamin Lorent, 2010. "Insurance Solvency Regulation: Regulatory Approaches Compared," Working Papers CEB 10-041, ULB -- Universite Libre de Bruxelles.
    7. Hoelle, Matthew, 2017. "The effects of dependent beliefs on endogenous leverage," Journal of Mathematical Economics, Elsevier, vol. 73(C), pages 68-80.
    8. Diers, Dorothea & Eling, Martin & Marek, Sebastian D., 2012. "Dependence modeling in non-life insurance using the Bernstein copula," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 430-436.

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