Scale Adjustments to Excess Expected Losses

Loss distributions underlying increased limits factors are usually based on countrywide data, as state/class information is generally regarded as too sparse for this purpose. Yet the state/class average severities may be reliable, and the countrywide distributions can be adjusted for differences in this average, for example, by assuming that all losses move in the same proportion. Such a scale change model can yield state/class increased limits factors; however, in many cases a single factor can be derived to adjust the countrywide increased limit factor incremental differences for the state or class average severity differential. This serves to appreciably simplify the application of the scale change model. A complication arises in the case of Commercial Automobile Combined Single Limits: besides the BI and PD average severity differentials, the relative frequencies of BI and PD losses vary by state/class, leading to differences in the overall BI-PD mix of losses, and thus in the relationship between basic limits and excess losses. With reasonable additional assumptions, the required change in CSL increased limit factor incremental differences can again be represented by a constant factor which, in this case, reflects mix as well as scale differences. Reinsurance Research - Loss Distributions, Size of