Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-23T17:59:09.918Z Has data issue: false hasContentIssue false
  • English
  • Français

FUNDAMENTAL DEFINITION OF THE SOLVENCY CAPITAL REQUIREMENT IN SOLVENCY II

Published online by Cambridge University Press:  07 May 2014

Marcus C. Christiansen  and
Andreas Niemeyer
Marcus C. Christiansen
Affiliation:
Institut für VersicherungswissenschaftenUniversität Ulm, D-89069 Ulm, Germany E-Mail: [email protected]
Andreas Niemeyer*
Affiliation:
Institut für VersicherungswissenschaftenUniversität Ulm, D-89069 Ulm, Germany
*
E-Mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

It is essential for insurance regulation to have a clear picture of the risk measures that are used. We compare different mathematical interpretations of the Solvency Capital Requirement (SCR) definition from Solvency II that can be found in the literature. We introduce a mathematical modeling framework that enables us to make a mathematically rigorous comparison. The paper shows similarities, differences, and properties such as convergence of the different SCR interpretations. Moreover, we generalize the SCR definition to future points in time based on a generalization of the value at risk. This allows for a sound definition of the Risk Margin. Our study helps to make the Solvency II insurance regulation more consistent.

Keywords

Solvency IISolvency Capital RequirementRisk Margindynamic value at riskminimal SCR
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 44 , Issue 3 , September 2014 , pp. 501 - 533
Copyright
Copyright © ASTIN Bulletin 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Artzner, P., Delbaen, F. and Koch-Medina, P. (2009) Risk measures and efficient use of capital. Astin Bulletin, 39 (1), 101.CrossRefGoogle Scholar
Artzner, P. and Eisele, K. (2010) Supervisory insurance accounting: Mathematics for provision - and solvency capital - requirement. Astin Bulletin, 40 (2), 569–585.Google Scholar
Barrieu, P., Bensusan, H., El Karoui, N., Hillairet, C., Loisel, S., Ravanelli, C. and Salhi, Y. (2012) Understanding, modelling and managing longevity risk: Key issues and main challenges. Scandinavian actuarial journal, 2012 (3), 203–231.CrossRefGoogle Scholar
Bauer, H. (1981) Probability Theory and Elements of Measure Theory. London: Academic Press.Google Scholar
Bauer, D., Reuss, A. and Singer, D. (2012) On the calculation of the solvency capital requirement based on nested simulations. Astin Bulletin, 42 (2), 453–499.Google Scholar
CEIOPS (2009) Final CEIOPS' Advice for Level 2 Implementing Measures on Solvency II: Technical Provisions – Article 86 (d) Calculation of the Risk Margin QIS 5 Technical Specifications. https://eiopa.europa.eu/fileadmin/tx_dam/files/consultations/consultationpapers/CP42/CEIOPS-L2-Final-Advice-on-TP-Risk-Margin.pdf.Google Scholar
CEIOPS (2010) QIS 5 Technical Specifications. https://eiopa.europa.eu/fileadmin/tx_dam/files/consultations/QIS/QIS5/QIS5-technical_specifications_20100706.pdf.Google Scholar
Devineau, L. and Loisel, S. (2009) Risk aggregation in Solvency II: How to converge the approaches of the internal models and those of the standard formula? Bulletin Français d'Actuariat, 9 (18), 107–145.Google Scholar
Devolder, P. (2011) Revised version of: Solvency requirement for long term guarantee: risk measure versus probability of ruin. European Actuarial Journal, 1 (2), 200–214.Google Scholar
Doff, R. (2008) A critical Analysis of the Solvency II proposals. The Geneva Papers on Risk and Insurance - Issues and Practice, 33 (2), 193–206.CrossRefGoogle Scholar
Eling, M., Schmeiser, H. and Schmit, J. (2007) The Solvency II process: Overview and critical analysis. Risk Management and Insurance Review, 10 (1), 69–85.Google Scholar
European Parliament and the Council (2009) Directive of the European Parliament and of the Council on the taking-up and pursuit of the business of insurance and reinsurance (Solvency II).Google Scholar
Filipović, D. (2009) Multi-level risk aggregation. Astin Bulletin, 39 (2), 565–575.Google Scholar
Floreani, A. (2011) Risk margin estimation through the cost of capital approach: Some conceptual issues. The Geneva Papers on Risk and Insurance - Issues and Practice, 36 (2), 226–253.Google Scholar
Holzmüller, I. (2009) The United States RBC standards, Solvency II and the Swiss Solvency Test: A comparative assessment. The Geneva Papers on Risk and Insurance - Issues and Practice, 34 (1), 56–77.Google Scholar
Kechris, A. (1995) Classical Descriptive Set Theory. New York: Springer.Google Scholar
Kochanski, M. (2010) Solvency capital requirement for German unit-linked insurance products. German Risk and Insurance Review, 6, 33–70.Google Scholar
Kriele, M. and Wolf, J. (2007) On market value margins and cost of capital. Blätter der DGVFM, 28 (2), 195–219.CrossRefGoogle Scholar
Kriele, M. and Wolf, J. (2012) Wertorientiertes Risikomanagement von Versicherungsunternehmen. Berlin: Springer.CrossRefGoogle Scholar
Milbrodt, H. (2010) Wahrscheinlichkeitstheorie - Eine Einführung mit Anwendungen und Beispielen aus der Versicherungs- und Finanzmathematik. Karlsruhe: Verlag Versicherungswirtschaft.Google Scholar
Möhr, C. (2011) Market-consistent valuation of insurance liabilities by cost of capital. Astin Bulletin, 41 (2), 315–341.Google Scholar
Ohlsson, E. and Lauzeningks, J. (2009) The one-year non-life insurance risk. Insurance: Mathematics and Economics, 45 (2), 203–208.Google Scholar
Salzmann, R. and Wüthrich, M. (2010) Cost-of-capital margin for a general insurance liability runoff. Astin Bulletin, 40 (2), 415–451.Google Scholar
Sandström, A. (2006) Solvency: Models, Assessment and Regulation. Boca Raton: Chapman & Hall/CRC Press.Google Scholar
Sandström, A. (2011) Handbook of Solvency for Actuaries and Risk Managers: Theory and Practice. Boca Raton: Chapman & Hall/CRC Press.Google Scholar
Steffen, T. (2008) Solvency II and the work of CEIOPS. The Geneva Papers on Risk and Insurance - Issues and Practice, 33 (1), 60–65.CrossRefGoogle Scholar
Wüthrich, M., Bühlmann, H. and Furrer, H. (2010) Market-Consistent Actuarial Valuation. Berlin: Springer.Google Scholar
Wüthrich, M., Embrechts, P. and Tsanakas, A. (2011) Risk margin for a non-life insurance run-off. Statistics & Risk Modeling, 28 (4), 299–317.CrossRefGoogle Scholar
Wüthrich, M. V. and Merz, M. (2013) Financial Modeling, Actuarial Valuation and Solvency in Insurance. Berlin: Springer.Google Scholar