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

A NEW METHOD OF ESTIMATING LOSS RESERVES 465The objective of this paper is to provide reserving actuarieswith a method or process to assist them with their “best guess”in the early years of development and with loss reserving ingeneral. The method introduced fundamentally is different fromother loss reserving methods because it explicitly assumes theevolution of the incremental incurred loss for an accident year isthe result of a random split of the ultimate loss for that accidentyear into separate pieces of losses that are observed in each developmentyear over the claim settlement period. The nature ofthe random split and the pattern of the evolution of incrementalincurred loss must be specified by the reserving actuary, thus givingthe method tremendous flexibility. As this method providesloss development factors without any knowledge of the distributionof the ultimate loss or of the actual cumulative incurredloss, it is suitable for calculating loss reserves for new lines ofbusiness, where there is little or no loss development data. Thismethod is suitable for paid and incurred loss, and can also beused in conjunction with the Bornhuetter-Ferguson method byproviding the necessary loss development factors.2. THE BASIC MODELAs is common in many models of the property/casualty lossreserving process, we assume: 41. The maximum number of years it takes for incurredlosses to be completely paid and settled is fixed andknown to be N, i.e., a claim occurring in accident year iis settled by the end of accident year i + N;2. The incremental loss development processes from differentaccident years are mutually independent, i.e., c ij andc kl are independent if i 6= k; and3. The incremental incurred loss in each accident yearforms a non-negative decreasing sequence, i.e.,4 This model can also be described in terms of paid losses.