Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T13:23:34.697Z Has data issue: false hasContentIssue false
  • English
  • Français

Economic capital modelling for the MTPL man-made catastrophe risk

Published online by Cambridge University Press:  04 September 2012

Werner Hürlimann
Werner Hürlimann*
Affiliation:
FRSGlobal Switzerland AG
*
*Correspondence to: Werner Hürlimann, FRSGlobal Switzerland AG, Seefeldstrasse 69, CH-8008 Zürich. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We undertake a mathematical clarification of the QIS5 proposal for the calculation of the Motor Third Party Liability (MTPL) man-made catastrophe risk capital in terms of two more general models. The QIS5 model assumption implies that the total loss consists of a single catastrophe claim in case it occurs during the next one-year insurance time period. However, the total loss should instead be dynamically modelled by a sequence of claims of varying size that follow a compound Poisson Pareto model, which is our first alternative model. A second possibility also takes into account the effect of investments, whose financial return process follows a Black-Scholes-Merton model. If one excludes limits of coverage, then asymptotically as the total loss increases without limits the first model is equivalent to the model assumption obtained from the QIS5 assumption by replacing a single catastrophe claim by the total loss. In other words, the QIS5 simple model is justified as limiting asymptotic approximation to the classical compound Poisson Pareto model. Conversely, an asymptotic approximation to the VaR economic capital from this model identifies with a modified QIS5 CAT formula. The inclusion of limits of coverage is also analyzed. In this situation we obtain new simple closed-form implementations of the economic capital formulas.

Keywords

economic capitalVaRcatastrophe riskMTPLcompound Poisson ParetoBlack-Scholes-Merton return modelclosed-form formula
Type
Papers
Information
Annals of Actuarial Science , Volume 7 , Issue 1: Special issue on Enterprise Risk Management , March 2013 , pp. 46 - 60
Copyright
Copyright © Institute and Faculty of Actuaries 2012

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

Berliner, B. (1985). Large risks and limits of insurability. The Geneva Papers on Risk and Insurance, 10(37), 313–329.Google Scholar
CEA CAT Risk (2011). CEA proposals for Catastrophe risk. URL: http://www.sff.is/media/cea/31.3.2011-CEA-proposals-for-Non-Life-Catastrophe-Risk.pdfGoogle Scholar
CEIOPS Calibration (2010). Solvency II Calibration Paper (15.4.2010). URL: https://eiopa.europa.eu/fileadmin/tx_dam/files/publications/submissionstotheec/CEIOPS-Calibration-paper-Solvency-II.pdfGoogle Scholar
CEIOPS CTF Report (2010). Catastrophe Task Force Report on standardized scenarios for the catastrophe risk module in the standard formula (11.6.2010). URL: https://eiopa.europa.eu/fileadmin/tx_dam/files/publications/submissionstotheec/CEIOPS-DOC-79-10-CAT-TF-Report.pdfGoogle Scholar
CP71 (2010). CEIOPS’ Advice for Level 2 Implementing Measures on Solvency II: SCR Standard Formula Calibration of Non-Life Underwriting Risk. CEIOPS-DOC-67/10, 8 April 2010. URL: https://eiopa.europa.eu/consultations/consultation-papers/index.htmlGoogle Scholar
Charpentier, A. (2007a). Modelling and covering catastrophic risks. AXA Risk College. URL: http://perso.univ-rennes1.fr/arthur.charpentier/slides-axa.pdfGoogle Scholar
Charpentier, A. (2007b). Insuring risks when pure premium is infinite? Bulletin Français d'Actuariat, 7(13), 67–82.Google Scholar
Directive 2009/138/EC (2009). Directive 2009/138/EC of the European Parliament and of the Council of 25 November 2009 on the taking-up and pursuit of the business of Insurance and Reinsurance (Solvency II). Official Journal of the European Union. URL: http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=OJ:L:2009:335:0001:0155:EN:PDFGoogle Scholar
EC-Draft L2 IM (2010). Consolidated text of EC's draft regulation for IMs. Insurance Asssociation of Cyprus. URL: http://www.iac.org.cy/easyconsole.cfm/id/283Google Scholar
Hürlimann, W. (2003). Conditional value-at-risk bounds for compound Poisson risks and a normal approximation. Journal of Applied Mathematics, 3(3), 141–154.Google Scholar
Hürlimann, W. (2006). Fitting return periods for largest claims with a Fréchet copula: a case study. 28th Int. Congress of Actuaries, Paris.Google Scholar
Hürlimann, W. (2007). Benchmark rates for XL reinsurance revisited: model comparison for the Swiss MTPL market. Belgian Actuarial Bulletin, 7(1), 1–9. URL: http://www.belgianactuarialbulletin.be/articles/vol07/01-Hurlimann.pdfGoogle Scholar
Hürlimann, W. (2010). Modelling non-life insurance risk for Solvency II in a reinsurance context. Life & Pensions Magazine, January 2010, 35–40.Google Scholar
Hürlimann, W. (2011). Insurance risk capital for the Sparre Andersen model with geometric Lévy stochastic returns. European Actuarial Journal, Online first, September 15.CrossRefGoogle Scholar
QIS5 (2010). Technical Specifications QIS5 – EIOPA Quantitative Impact Study 5. URL: https://eiopa.europa.eu/consultations/qis/quantitative-impact-study-5/index.htmlGoogle Scholar
QIS5 errata (2010). Errata to the QIS5 Technical Specifications. URL: http://ec.europa.eu/internal_market/insurance/docs/solvency/qis5/201007/technical_specifications_errata_en.pdfGoogle Scholar
Strassburger, D. (2006). Risk Management and Solvency – Mathematical Methods in Theory and Practice. Ph.D. Thesis, Carl von Ossietzky University of Oldenburg. URL: http://oops.uni-oldenburg.de/volltexte/2007/81/pdf/strris06.pdfGoogle Scholar
Sundt, B., Vernic, R. (2009). Recursions for convolutions and compound distributions with insurance applications. EAA Lecture Notes, vol. 2, Springer-Verlag.Google Scholar
Zajdenweber, D. (1996). Extreme values in business interruption insurance. Journal of Risk and Insurance, 1, 95–110.Google Scholar