PEBELS: Property Exposure Based Excess Loss Smoothing

The invention of PEBELS, or policy exposure based excess loss smoothing, was motivated by the need to develop estimates of high layer expected loss cost for extremely small, non-credible segments of a primary property book of business. The existing actuarial literature provides methods for estimating high layer excess loss cost for large property portfolios in aggregate, but does not provide a method to produce similar provisions for smaller subsets of such a book. PEBELS was developed to be just such a method. PEBELS generalizes existing pricing theory from published property per risk reinsurance exposure rating methods and leverages increasingly available exposure data to produce a method which allows the practitioner to develop accurate high layer expected loss cost estimates down to the policy level. Once the theoretical framework required to implement this method in practice has been formulated, his paper continues to explore applications of PEBELS outside of primary insurance pricing where granular segmentation of expected loss by layer would refine results, such as adjusting modeled catastrophe average annual losses (AALs) for bias from implicit linearity assumptions, improving the predictiveness of property predictive models including generalized linear models (GLMs), and refining the published property per risk reinsurance exposure rating method.

Motivation. Develop a practical method to determine property large loss provisions.

Method. Property exposure analysis.

Results. The PEBELS method of developing property large loss provisions, for use in any application requiring segmentation between primary and excess property loss layers.

Conclusions. PEBELS is a practical theory of property large loss exposure.

Availability. N/A

Keywords. Property, Ratemaking, Large Loss, Excess Loss, Catastrophe, Average Annual Loss, AAL, Predictive Modeling, Generalized Linear Model, GLM, Reinsurance, Exposure Rating, Property Per Risk Reinsurance, PPR