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

ESTIMATING THE WORKERS COMPENSATION TAIL 661The first column to the right of the age-at-injury values isa portion of the distribution of 750 male PD claimants by age,based on individual permanent total disability (PTD) claimantdata from SAIF for accident years 1975 through 1990. We assumedthat the age-at-injury distribution for PD claims wouldbe the same as for PTD claims. The actual census data weresmoothed among different age-at-injury categories to derive thenumbers in Column (1).Consider the row for the age-at-injury of 40. Suppose that12.99 of the 1,000 total claimants were injured at age 40. Theprobability of living from age 40 to age 41 from the male 2000SSA mortality table is used to calculate the expected numberof male claimants still alive one year after the accident, and soforth for each subsequent age and year of development out todevelopment year 90. In this way each age-at-injury row is filledout in the array. For each development year column, the expectedtotal number of surviving claimants is simply the sum of theexpected number of surviving claimants for each age-at-injuryranging from 40 through 49.The same calculations were performed for all possible agesat-injuryand all development years from 1 through 90. The resultingestimates of the number of surviving male claimants issummarized in Table C.2.2 for different age-at-injury groupingsat different selected years of development. The totals derivedin Table C.2.1 are displayed in the 40—49 age-at-injury row inTable C.2.2.In Table C.2.2, the expected number of surviving claimants atthe beginning of development year 5 is 722.1 and at developmentyear 10 is 674.4. Hence the probability of survival during the fifththrough ninth development years for all male claimants is 93.4%.It is evident from a review of the bottom row of Table C.2.2that the survival probabilities steadily decline as the claimantpopulation ages.