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

A NEW METHOD OF ESTIMATING LOSS RESERVES 463TABLE 1Loss Development TriangleDevelopment Year (j)AccidentYear (i) 0 1 2 ¢¢¢ k ¡ 1 k1 C 10 C 11 C 12 ¢¢¢ C 1,k¡1 C 1k2 C 20 C 21 C 22 ¢¢¢ C 2,k¡1....k ¡ 1 C k¡1,0 C k¡1,1k C k,0form of a loss development triangle as shown in Table 1. A basicassumption in loss reserving is that the data in the rows of Table 1are mutually independent, i.e., C ij and C rm are independent ifi 6= r. In other words, losses from different accident years evolveindependently. Another assumption is that all losses are settledwithin a certain number of calendar years, N years, say, fromtheir date of occurrence, regardless of the year of occurrence.This means that C ij = C iN for j ¸ N and i =1,2,:::. Sometimes,however, the data in the loss development triangle consist ofincremental incurred losses, c ij ,where(Cij ¡ C i,j¡1 j =1,2,:::c ij =C i0 j =0:The decision to use either incremental or cumulative values dependson the loss reserving method used.Given C ij , the ultimate incurred loss for accident year i, S i ,isestimated as:S i = C ij £ LDF j (1)where LDF j is the incurred loss development factor for developmentyear j to ultimate. When the total paid loss for occurrenceyear i at the end of development year j (TPL ij ) is known, the