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A GENERALISED PROPERTY EXPOSURE RATING FRAMEWORK THAT INCORPORATES SCALE-INDEPENDENT LOSSES AND MAXIMUM POSSIBLE LOSS UNCERTAINTY

Published online by Cambridge University Press:  18 May 2020

Pietro Parodi Open the ORCID record for Pietro Parodi [Opens in a new window]
Pietro Parodi*
Affiliation:
SCOR Business Solutions, 10 Lime Street, LondonEC3M 7AA, UK, E-mail: [email protected]
*
E-mail: [email protected]
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Abstract

A generalised property exposure rating framework is presented here to address two issues arising in the standard approach to exposure rating, especially in the context of direct insurance and facultative reinsurance (D&F) property pricing:

  1. (a) What to do when the main assumption of exposure rating, scalability – that is, that the probability of a given damage ratio does not depend on the maximum possible loss (MPL) but only on the type of property – breaks down.

  2. (b) How to take account of the uncertainty around the MPL, that is, the fact that the MPL (unlike the insured value, IV) is an informed estimate rather than a contractual feature.

The first difficulty is addressed by making the exposure rating framework more flexible by introducing exposure curves that are a mixture of scale-dependent and scale-independent losses, and where the weight given to the two components is a function of the MPL. This allows to model the impact on the expected losses of changes in the underlying deductibles, a classic problem in D&F pricing normally solved with the help of deductible impact tables. The second difficulty is addressed by working out the mathematical implications of having a finite probability of exceeding the MPL and extending the exposure curve up to the maximum of MPL and IV. A practical application of this framework – in which the scale-independent and scale-dependent losses are identified with attritional and large losses respectively – is described. A discussion of how this generalised framework can be calibrated based on actual data is included, and implementation code for the framework is made available.

Keywords

Exposure curvesscale-independent lossesmaximum possible lossinsured valueimpact of deductible changes
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 2 , May 2020 , pp. 513 - 553
Copyright
© Astin Bulletin 2020

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References

Bernegger, S. (1997) The Swiss Re exposure curves and the MBBEFD distribution class. ASTIN Bulletin 27(1), 99–111.10.2143/AST.27.1.563208CrossRefGoogle Scholar
Bishop, C.M. (2006) Pattern Recognition and Machine Learning. New York: Springer.Google Scholar
Dempster, A., Laird, N. and Rubin, D. (1977) Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B (Methodological), 39(1), 1–38.10.1111/j.2517-6161.1977.tb01600.xCrossRefGoogle Scholar
Devroye, L. (1986) Non-Uniform Random Variate Generation. New York: Springer-Verlag.10.1007/978-1-4613-8643-8CrossRefGoogle Scholar
Dutang, C., Gesmann, M. and Spedicato, G. (2019) Exposure rating, destruction rate models and the MBBEFD package, https://cran.r-project.org/web/packages/mbbefd/vignettes/Introduction_to_mbbefd.pdf.Google Scholar
Guggisberg, D. (2004) Exposure Rating, Zurich: Swiss Re. http://www.swissre.com.Google Scholar
Lee, G.Y. and Frees, E.W. (2016) General insurance deductible ratemaking with applications to the local government property insurance fund, https://www.soa.org/resources/research-reports/2016/2016-deductible-ratemaking/.Google Scholar
Ludwig, S.J. (1991) An exposure rating approach to pricing property excess-of-loss reinsurance. Proceedings of the Casualty American Society, LXXVIII, 110–145.Google Scholar
Parodi, P. (2014a) Pricing in General Insurance, New York: CRC Press.10.1201/b17525CrossRefGoogle Scholar
Parodi, P. (2014b) Appendix 3 – Introduction to commercial property pricing, http://www.pricingingeneralinsurance.com/home/additional-text.Google Scholar
Parodi, P. (2019) http://www.pricingingeneralinsurance.com/home/downloads/genexposurerating.Google Scholar
Parodi, P. and Watson, P. (2019) Property graphs – A statistical model for fire and explosion losses based on graph theory. ASTIN Bulletin, 49(2), 263–297. doi: 10.1017/asb.2019.4.CrossRefGoogle Scholar
Riegel, U. (2010) On fire exposure rating and the impact of the risk profile type. ASTIN Bulletin 40(2), 727–777.Google Scholar
Salzmann, R.E. (1963) Rating by layer of insurance. Proceedings of the Casualty American Society, LXXVIII, 110–145.Google Scholar
Trudeau, R.J. (2003) Introduction to Graph Theory. New York: Dover Publications Inc.Google Scholar