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

246 WHEN CAN ACCIDENT YEARS BE REGARDED AS DEVELOPMENT YEARS?This applies generally when interchanging accident and developmentyears in the incremental paid loss array and applyingthe chain ladder. When considered in terms of the incrementalpaid loss formula, the transposition merely interchanges the valuesof B and C, andleavesA unchanged, so the incremental paidloss forecasts are unchanged.One advantage of this incremental paid loss version of thechain ladder is that it is often more convenient to implement ina spreadsheet. This is because it can be implemented in termsof formulas that can be successfully cut and pasted without theeffort involved in computing the ratios first. The usual ratios(and cumulative paid loss forecasts if needed) are then easilycomputed from the completed array.3. A BRIEF DISCUSSION OF SOME RELATED WORKKremer [4] recognizes the connection between a ratio model(which he calls a multiplicative model) and two-way analysis ofvariance with missing values, computed on the logarithms. Heuses this to derive an approach to forecasting outstanding claims.Kremer points out the connection to the chain ladder method indetail.Mack [5] derives standard error calculations (including processand parameter error) for a mean-variance model whose forecastsreproduce the standard chain ladder technique in a recursivefashion. Mack makes use of the Gauss-Markov theorem toavoid specific distributional assumptions for the losses. He comparesresults for a particular case study with results from similarmodels for which computation of exact or approximate standarderrors are available.In his later paper, Mack [6] argues that while several differentstochastic ratio models had previously been referred to as thestochastic chain ladder, the model he discusses in [5] reproduces