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

A NEW METHOD OF ESTIMATING LOSS RESERVES 475STEP 6. Order the N +1 Y j ’s as Y (1) · Y (2) :::· Y (N+1) .STEP 7.For j =0,1,2,:::,N, setjXTEMP (1)j,N =TEMP(1) j,N + E[Y (r )]r=0TEMP (2)j,N =TEMP(2) j,N + 1P jr=0 Y :( r )STEP 8.Repeat Steps 3 to 7 a total of M times.STEP 9. For j =0,1,2,:::,N, the loss development factors areestimated as:LDF d(1) Mj,N =(20)5.3. Other Practical ConsiderationsTEMP (1)j,NLDF d(2)j,N = TEMP(2) j,NM : (21)In practice, other potential problems may occur such as differentaccident years having different claim settlement periods.For example, N depends on i, or the existence of negative incrementalincurred loss amounts. Tables 6 and 7 display twohypothetical data sets with several problems. In Table 6, one canassume that losses are settled in three years, i.e., N =3. However,the losses do not exhibit the pattern assumed by Tables A1and A2. In fact, even though the losses are settled in 3 years, thetotal incurred loss changes only slightly after development year1, and for year 2001 the cumulative incurred loss is decreasing.Our method is not ideally suited to the data in Table 6 becauseof the negative incremental losses. Further research is needed inthis area.