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

596 ESTIMATING THE WORKERS COMPENSATION TAILple. This section describes the Mueller Incremental Tail (MIT)method and provides the formulas and key results. The actualcalculations are included in Appendix A.The MIT method was used to calculate empirical 37 to ultimatetail factors using the incremental data on old accident years.The empirical data ended at 65 years of development, which forpurposes of this section will be considered to be ultimate. Wedescribe the method in three stages:Notation:1. Incremental age-to-age decay ratios.2. Anchored decay factors.3. Tail factors.Let S n =Cumulative payments through n years of developmentp n =Incremental payments made in year n; andS n = P p i (i =1ton).Let PLDF n =Agen ¡ 1ton paid loss development factor.PLDF n = S n =S n¡1 =(S n¡1 + p n )=S n¡1 =1+p n =S n¡1 .Let f n = p n =S n¡1 ,thenPLDF n =1+f n .1. Incremental age-to-age decay ratios. The first step is tocalculate incremental age-to-age decay ratios: p n+1 =p n ,p n+2 =p n+1 , p n+3 =p n+2 , and so on. With the SAIF data,we are able to calculate ratios of incremental paid loss atage (n + 1) to incremental paid at age (n), for n rangingfrom 29 to 65, using 20-year weighted averages. Becauseof the sparseness of claims of this age, the empirical decayratios needed to be smoothed before they could beused. The smoothing was done using five-year centered