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

598 ESTIMATING THE WORKERS COMPENSATION TAILTABLE 2.2Cumulative Decay Factors Relative to IncrementalPayments During Different Anchor YearsAnchor YearCumulative Decay Factor37 30.07136 30.11535 29.50834 28.28033 26.961For example, payments made in DY 50 are, on average, almostdouble (88.0% greater) the payments made in DY 37.By summing the anchored decay factors from 38 to ultimate,we get the payments made in ages 38 to 65 relative to paymentsmade in year 37. We will refer to each of these as anchoredcumulative decay factors D n ,whereD n+1 = p n+1 =p n + p n+2 =p n + ¢¢¢= X d i :The sums of the decay factors are similar to tail factors, butinstead of being relative to cumulative payments they are relativeto the incremental payments made in the anchor year.The process can be repeated using a different anchor year. Inaddition to anchor year 37, the calculations were also performedusing anchor years 36, 35, 34, and 33. In each case, the paymentsfrom 38 to ultimate were compared to the payments made inthe selected anchor year. Table 2.2 shows the cumulative decayfactors for each of these anchor years.The cumulative decay factors can be interpreted as follows:Payments made from ages 38 to ultimate are 30.071 times thepayments made in age 37. Similarly, payments made in ages 38to ultimate are 30.115 times the payments made in age 36, andso on.