An Alternative Approach to Credibility for Large Account and Excess of Loss Treaty Pricing

This paper illustrates a comprehensive approach to utilizing and credibility weighting all available information for large account and excess of loss treaty pricing. The typical approach to considering the loss experience above the basic limit is to analyze the burn costs in these excess layers directly (see Clark 2011, for example). Burn costs are extremely volatile in addition to being highly right skewed, which does not perform well with linear credibility methods, such as Buhlmann-Straub or similar methods (Venter 2003). Using burn costs also involves developing and making a selection for each excess layer, which can be cumbersome. Also the formulas for calculating all of the correlations needed for determining the credibilities are complicated.

An alternative approach is shown that uses all of the available data in a more robust and seamless manner. Credibility weighting of the account’s experience with the exposure cost for the basic limit is performed using Buhlmann-Straub credibility. Modified formulae are shown that are more suitable for this scenario. For the excess layers, the excess losses themselves are utilized to modify the severity distribution that is used to calculate the increased limit factors. This is done via a simple Bayesian credibility technique that does not require any specialized software to run. Such an approach considers all available information in the same way as analyzing burn costs, but does not suffer from the same pitfalls. Certain modifications are also illustrated to produce a method that does not differentiate between basic limit and the excess losses. Lastly, it is shown how the method can be improved for higher layers by leveraging Extreme Value Theory.

Keywords: Buhlmann-Straub Credibility, Bayesian Credibility, Loss Rating, Exposure Rating, Burn Cost, Extreme Value Theory