An Alternative Approach to Credibility for Large Account Pricing
By Uri A. Korn
This paper discusses an alternative approach to utilizing and credibility weighting the excess loss information for large account pricing. The typical approach is to analyze the burn costs in each excess layer 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). An alternative approach is shown that uses all of the available data in a more robust and seamless manner where 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.
Keywords Buhlmann-Straub credibility, Bayesian credibility, loss rating, exposure rating, burn cost, extreme value theory