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

A NEW METHOD OF ESTIMATING LOSS RESERVES 477TABLE 8Loss Development Factors (C i,j+1 =C i,j )fromTable7Development Year (j=j +1)AccidentYear 0/1 1/2 2/3 3/4 4/5 5/61996 0.8615 1.0000 1.0259 1.0095 1.1323 1.00001997 1.2466 1.0997 0.9870 0.9421 1.14101998 1.2583 1.1667 1.0719 1.00721999 1.2967 1.1702 0.98082000 1.3656 1.24192001 1.09312002year i, S i , can still be estimated asS i = P jk=0 Y : (22)(N i +1¡k)Note, the length of the claim settlement period can be approximatedby observing cumulative loss development factors. If theassumptions of this model (as stated in Section 2) hold, then thejth annual cumulative loss development factor for accident yeari, C i,j+1 =C i,j , should satisfyC i,j+1C ijj,NLDF (k)j+1,NC i,j¼ LDF(k)(23)for k =1,2 and j =0,1,:::N ¡ 1. Table A2 shows the valuesLDF (k)j,N =LDF(k) j+1,Nfor k =1,2, j =0,1,:::,9 and N =1,2,:::,9.The annual cumulative loss development factors should then becompared with those in Table A2. Table 8 shows the actual cumulativeloss development factors generated by Table 7. Comparingthe first two columns of Table 8 with those expected inTable A2 show that patterns of actual cumulative loss developmentfactors for years 1997 to 2001 are too low, making the datain Table 7 inconsistent with the assumption of a uniform randomsplit. Notice that the results of Tables A3 and A4 for ¸ =5seem