The Luxemburg XL and SL premium principle

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Werner Hürlimann, Suisse
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Summary:
According to the regulation of reinsurance companies in Luxemburg, any such company must, for all its activities, constitute a provision for fluctuation of claims. The multiple of a risk or portfolio of risks is equal to the half-number above the sextuple of the standard deviation of the ratio of claims burden to premiums received and should not exceed 17.5. A general method for the calculation of multiples for excess-of-loss (XL) and stop-loss (SL) reinsurance for individual contracts and portfolios of independent contracts is presented. It is remarkable that the multiple of an excess-of-loss layer can be approximated using a simple proposal by Benktander(1975) to evaluate the standard deviation of a limited XL layer. For a wide range of parameter values, the approximate multiple differs from its theoretical value by a negligible quantity of +/- 0,5. Distribution-free results and a multivariate generalization are also presented.
 
Date: 30 May - Time: 10:30 to 12:00 - Room: 241
Theme: 3.B. High severity risks and insurability