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

470 A NEW METHOD OF ESTIMATING LOSS RESERVESTABLE 2Hypothetical Cumulative Incurred and Paid Losses(in 000s)Development Year (j)Earned Incurred Loss (C ij )Paid LossAccident PremiumsYear (i) (in 000s) 0 1 2 0 1 22000 4,500 1,447 1,976 2,454 401 1,166 1,7612001 8,500 3,578 3,911 906 2,5732002 16,000 4,754 1,7192000—2002, as of December 31, 2002, is:Ŝ (1) = 4,754 £ 1:9195 + 3,911 £ 1:2627 + 2,454 £ 1:0662= 16,680:18Ŝ (2) = 4,754 £ 2:0379 + 3,911 £ 1:2826 + 2,454 £ 1:0691= 17,328:00using the N = 3 rows of Table A1. The corresponding reserveestimates are 10,627:18 = 16,680:18 ¡ 6,053 and 11,275:00 =17,328:00 ¡ 6,053, respectively.If, on the other hand, we assume N = 5, then the estimatedultimate loss for 2000—2002, as of December 31, 2002, is:Ŝ (1) = 4,754 £ 2:4564 + 3,911 £ 1:5412 + 2,454 £ 1:2384= 20,744:39Ŝ (2) = 4,754 £ 2:6221 + 3,911 £ 1:5800 + 2,454 £ 1:2505= 21,713:57using the N = 5 row of Table A1. These ultimates lead to reserveestimates of 14,691:39 = 20,744:39 ¡ 6,053, and 15,660:57 =21,713:57 ¡ 6,053, respectively.