PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

WHEN CAN ACCIDENT YEARS BE REGARDED ASDEVELOPMENT YEARS?GLEN BARNETT, BEN ZEHNWIRTH AND EUGENE DUBOSSARSKYAbstractThe chain ladder (volume-weighted average developmentfactor) is perhaps the most widely used of the linkratio (age-to-age development factor) techniques, beingpopular among actuaries in many countries. The chainladder technique has a number of interesting properties.We present one such property, which indicates that thechain ladder doesn’t distinguish between accident yearsand development years. While we have not seen a proofof this property in English language journals, it appearsin Dannenburg, Kaas and Usman [2]. The result is alsodiscussed in Kaas et al. [3]. We give a simple proof thatthe chain ladder possesses this property and discuss itsimplications for the chain ladder technique. It becomesclear that the chain ladder does not capture the structureof real triangles.1. INTRODUCTIONLink ratio (loss development factor) methods are widely usedfor reserving. The chain ladder technique is one such method appliedto cumulative paid loss (or sometimes case incurred loss).The development factor is an average of the individual link ratios,weighted by the previous cumulative loss (volume-weightedaverage). The chain ladder is normally applied to cumulatedpaid loss arrays, incurred loss arrays, or sometimes to cumulatedclaim numbers, such as claims incurred, claims notified orclaims closed. This “formal” chain ladder is described by Mackin [5], but we give a detailed description of it below. We presentthe chain ladder for a paid loss array with annual data; the expo-239