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TEST FOR CHANGES IN THE MODELED SOLVENCY CAPITAL REQUIREMENT OF AN INTERNAL RISK MODEL

Published online by Cambridge University Press:  06 August 2021

Daniel Gaigall
Daniel Gaigall*
Affiliation:
Institute of Probability and Statistics, Leibniz University Hannover, Welfengarten 1, 30167 Hannover, Germany, E-Mail: gaigall@stochastik.uni-hannover.de House of Insurance, Leibniz University Hannover, Welfengarten 1, 30167 Hannover, Germany, E-Mail: daniel.gaigall@insurance.uni-hannover.de Group Risk Management, HDI Service AG, HDI-Platz 1, 30659 Hannover, Germany, E-Mail: daniel.gaigall@hdi.de
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Abstract

In the context of the Solvency II directive, the operation of an internal risk model is a possible way for risk assessment and for the determination of the solvency capital requirement of an insurance company in the European Union. A Monte Carlo procedure is customary to generate a model output. To be compliant with the directive, validation of the internal risk model is conducted on the basis of the model output. For this purpose, we suggest a new test for checking whether there is a significant change in the modeled solvency capital requirement. Asymptotic properties of the test statistic are investigated and a bootstrap approximation is justified. A simulation study investigates the performance of the test in the finite sample case and confirms the theoretical results. The internal risk model and the application of the test is illustrated in a simplified example. The method has more general usage for inference of a broad class of law-invariant and coherent risk measures on the basis of a paired sample.

Keywords

BootstrapEmpirical processFunctional Delta methodHadamard differentiabilityPaired sample
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 3 , September 2021 , pp. 813 - 837
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The International Actuarial Association

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