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On the Calculation of the Solvency Capital Requirement Based on Nested Simulations*

Published online by Cambridge University Press:  09 August 2013

Daniel Bauer
Department of Risk Management and Insurance, Georgia State University, 35 Broad Street. Atlanta, GA 30303. USA, Tel.: +1-404-413-7490, Fax: +1-404-413-7499, E-Mail:
Andreas Reuss
Institute for Finance and Actuarial Sciences (ifa), Helmholtzstrasse 22. 89081 Ulm.Germany, Tel.: +49-(731)-50-31251, Fax: +49-(731)-50-31239, E-Mail:
Daniela Singer
Institute for Finance and Actuarial Sciences (ifa), Helmholtzstrasse 22. 89081 Ulm.Germany, Tel.: +49-(731)-50-31259, Fax: +49-(731)-50-31239, E-Mail:


Within the European Union, risk-based funding requirements for insurance companies are currently being revised as part of the Solvency II project. However, many life insurers struggle with the implementation, which to a large extent appears to be due to a lack of know-how regarding both, stochastic modeling and efficient techniques for the numerical implementation.

The current paper addresses these problems by providing a mathematical framework for the derivation of the required risk capital and by reviewing different alternatives for the numerical implementation based on nested simulations. In particular, we seek to provide guidance for practitioners by illustrating and comparing the different techniques based on numerical experiments.

Research Article
Copyright © International Actuarial Association 2012

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Parts of this paper are taken from an earlier paper called “Solvency II and Nested Simulations — a Least-Squares Monte Carlo Approach” and from the third author's doctoral dissertation (cf. Bergmann (2011)). The authors are grateful for helpful comments from an anonymous referee and seminar participants at the 2009 ARIA meeting, the 2009 CMA Workshop on Insurance Mathematics and Longevity Risk, the 2010 International Congress of Actuaries, Georgia State University, Humboldt University of Berlin, Ulm University, and the University of Duisburg-Essen. All remaining errors are ours.


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