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

654 ESTIMATING THE WORKERS COMPENSATION TAILBecause this approach produces volatile indicated tail factors,Table A.6 presents an approach for stabilizing those indications(see Table 2.6). Each of the average PLDFs for ages 30 through36 are adjusted to what they would be for age 37 using theappropriate products of incremental decay factors from AY 1965and prior years. A weighted average of all of these adjustedPLDFs is then used to replace the actual PLDF for DY 37. Inthis way, the PLDF for DY 37 is changed from being entirelydetermined by only one historical PLDF for one AY, to being anindication based on all 36 PLDFs for DYs 30 through 37. Thisresults in a reduction of the PLDF for anchor year 37 from 1.033to 1.022. The final selected tail factor from age 37 to 65 is then1 plus the product of 0.022/1.022, the cumulative decay factorof 30.071 and 1/1.022 (= 1:634).Once the best estimate of the PLDF for the anchor year (DY37) is selected, then all of the subsequent PLDFs can be easilygenerated using the iterative formula:f n+1 = f n d n+1 =[1 + f n ],where f n is the paid loss development factor, less one, for thenth year of development, and d n+1 is the decay ratio betweenincremental paid during year (n + 1) and year (n). See Section 2for a derivation of this formula.3. Tail factors. Tail factors can be calculated either by cumulatingthe age-to-age PLDFs calculated above or directlyfrom the cumulative decay factors D n+1 linked toan age-to-age factor f n from the cumulative triangle usingthe formulaTail factor n = f n D n+1 =[1 + f n ],where D n+1 is the cumulative decay factor calculatedfrom the incremental data, and f n is derived from thenormal cumulative triangle. See Section 2.