Comparison of Severity Estimators’ Efficiency Based on Different Data Aggregation Levels

Estimates of the ultimate claim value occur in many actuarial models. Detailed data about each claim are available for estimation: each claim is at first booked at an initial value and processed over a random number of years, during which it is adjusted until closure. The ultimate value can be estimated based on observations of the ultimate value directly, which in this context, means using aggregated data. A more detailed, distribution-free estimator based on estimates of the initial claim value, the closure probability, and development factors is constructed in this article. It is proved that this estimator is asymptotically unbiased and an approximate analytical formula is derived for its variance. The efficiency of this estimator is compared to the efficiency of the simple arithmetic average of the ultimate claim value. Results are illustrated on an example and complemented with a simulation. The example results in significantly lower variability of the detailed estimator.