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Operational Choices for Risk Aggregation in Insurance: PSDization and SCR Sensitivity

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  • Xavier Milhaud

    (Universite de Lyon, Université Claude Bernard Lyon 1, Institut de Science Financiere et d’Assurances, Laboratoire de Sciences Actuarielle et Financiere, F-69007 Lyon, France
    The views expressed herein reflect solely those of their authors.)

  • Victorien Poncelet

    (Banque de France, 61 rue Taitbout, 75009 Paris, France
    The views expressed herein reflect solely those of their authors.)

  • Clement Saillard

    (BNP Paribas Cardif, RISK, 10 rue du Port, 92000 Nanterre, France
    The views expressed herein reflect solely those of their authors.)

Abstract

This work addresses crucial questions about the robustness of the PSDization process for applications in insurance. PSDization refers to the process that forces a matrix to become positive semidefinite. For companies using copulas to aggregate risks in their internal model, PSDization occurs when working with correlation matrices to compute the Solvency Capital Requirement (SCR). We examine how classical operational choices concerning the modelling of risk dependence impacts the SCR during PSDization . These operations refer to the permutations of risks (or business lines) in the correlation matrix, the addition of a new risk, and the introduction of confidence weights given to the correlation coefficients. The use of genetic algorithms shows that theoretically neutral transformations of the correlation matrix can surprisingly lead to significant sensitivities of the SCR (up to 6%). This highlights the need for a very strong internal control around the PSDization step.

Suggested Citation

  • Xavier Milhaud & Victorien Poncelet & Clement Saillard, 2018. "Operational Choices for Risk Aggregation in Insurance: PSDization and SCR Sensitivity," Risks, MDPI, vol. 6(2), pages 1-23, April.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:2:p:36-:d:141009
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    References listed on IDEAS

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    1. Laurent Devineau & Stéphane Loisel, 2009. "Risk aggregation in Solvency II: How to converge the approaches of the internal models and those of the standard formula?," Post-Print hal-00403662, HAL.
    2. Denuit, M. & Genest, C. & Marceau, E., 1999. "Stochastic bounds on sums of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 85-104, September.
    3. Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
    4. Stefan Cutajar & Helena Smigoc & Adrian O’Hagan, 2017. "Actuarial Risk Matrices: The Nearest Positive Semidefinite Matrix Problem," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(4), pages 552-564, October.
    5. Bernard, Carole & Jiang, Xiao & Wang, Ruodu, 2014. "Risk aggregation with dependence uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 93-108.
    6. Filipović, Damir, 2009. "Multi-Level Risk Aggregation," ASTIN Bulletin, Cambridge University Press, vol. 39(2), pages 565-575, November.
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