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

620 ESTIMATING THE WORKERS COMPENSATION TAILTABLE 5.3Number of Open Claims for Representative AccidentYearsatFive-YearIntervalsofDevelopmentEnd of Development YearAY 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 801970 653 196 149 119 95 71 50 33 21 12 6.9 3.5 1.5 0.5 0.1 0.021975 655 197 150 120 97 73 52 34 22 13 7.2 3.7 1.6 0.6 0.1 0.031980 659 200 153 123 100 76 54 36 23 14 7.7 3.9 1.7 0.6 0.2 0.031985 662 202 156 126 103 79 56 38 24 14 8.1 4.2 1.9 0.7 0.2 0.041990 665 204 158 128 105 81 58 39 25 15 8.5 4.4 2.0 0.7 0.2 0.041995 668 206 160 130 108 83 60 41 26 16 9.0 4.7 2.1 0.8 0.2 0.052000 670 207 161 132 110 86 62 42 27 17 9.5 5.0 2.3 0.9 0.3 0.06TABLE 5.4Percentage Increases in the Number of Open Claims atthe End of Representative Development Years–fromAccident Year 1970 to Accident Year 2000End of Development Year5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 802.6 5.6 8.3 11.6 15.6 19.8 23.9 27.4 30.3 33.5 37.5 43.7 54.3 73.2 106.8 164.5increases as one moves from the earlier development years onthe left to the later development years on the right. This is due tothe compounding effect of expected declines in future mortalityrates. Table 5.4 displays the total percentage increase for eachdevelopment year column.Since the number of open claims at any given developmentyear will be increasing steadily over successive accident years,the total proportion of ultimate losses paid through that developmentyear will decline slightly over time. Because of this wewould naturally expect that the appropriate tail factors at anygiven development year will also increase steadily over time.The projected results are displayed in Table 5.5.