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

Xavier Milhaud, Victorien Poncelet and Clement Saillard
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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
Victorien Poncelet: Banque de France, 61 rue Taitbout, 75009 Paris, France
Clement Saillard: BNP Paribas Cardif, RISK, 10 rue du Port, 92000 Nanterre, France

Risks, 2018, vol. 6, issue 2, 1-23

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.

Keywords: solvency II; risk aggregation; positive semi-definite; Rebonato–Jäckel (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:6:y:2018:i:2:p:36-:d:141009

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