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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: werner.huerlimann@frsglobal.com
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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

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