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

ESTIMATING THE WORKERS COMPENSATION TAIL 5993. Tail factors. To convert these cumulative decay factorsinto tail factors, we make use of the selected cumulativeloss development factors from the customary cumulativepaid loss development triangle.The tail factor from n to ultimate= S 8 =S n=(S n + X p i )=S n=1+ X p i =S n=1+p n+1 =S n + p n+2 =S n + ¢¢¢=1+p n =S n (p n+1 =p n + p n+2 =p n + ¢¢¢):But p n =S n =(p n =S n¡1 )=(S n =S n¡1 )=f n =(1 + f n ), so thetail factor is 1 + [f n =(1 + f n )] £ D n+1 .The general formula for the tail factor at age n isTail factor n = f n D n+1 =[1 + f n ],where f n is the PLDF, less one, for the nth year of development,and D n+1 is the cumulative decay factor forpayments made during years n + 1 to ultimate relative topayments made in anchor year n.In a similar way, an age-to-age loss development factor (less 1.0)extending beyond the cumulative triangle isf n+1 = f n d n+1 =[1 + f n ],where d n+1 is the decay factor for payments made in year n +1relative to payments made in anchor year n.This method is sensitive to f n , the 37:36 PLDF less 1. Forthis reason the analysis can be repeated using the 36, 35, 34, or33 anchor years. Table 2.3 shows the 37 to ultimate tail factorcalculated using each of these anchor years.