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

A NEW METHOD OF ESTIMATING LOSS RESERVESCOLIN M. RAMSAYAbstractThis paper introduces a new method for estimatingloss reserves. The method is fundamentally different fromother loss reserving methods because it explicitly assumesthat the evolution of the incremental incurred lossfor an accident year is the result of a random split ofthe ultimate loss for that accident year into separatepieces that are observed in each development year overthe claim settlement period. The nature of the randomsplit and the pattern of the evolution of incremental incurredloss must be specified by the reserving actuary,thus giving the method tremendous flexibility. A key featureof this method is that it provides loss developmentfactors without any knowledge of the distribution of theultimate loss and without the actual cumulative incurredloss. Thus this method is suitable for calculating reservesfor new lines of business where there is little or no losssettlement data.1. INTRODUCTIONThe loss reserving problem can be briefly described as follows.Let S i denote the unknown ultimate incurred loss 1 for accidentyear i (excluding expected income from salvage and subrogation)and C ij denote the best estimate of cumulative incurredloss amounts for accident year i and development year 2 j.Thedata used to estimate loss reserves are usually presented in the1 The loss reserving problem can also be described in terms of cumulative paid losses orincurred but not reported (IBNR) losses.2 The development year refers to the number of calendar years as measured from theaccident year so that j = 0 refers to the accident year.462