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

240 WHEN CAN ACCIDENT YEARS BE REGARDED AS DEVELOPMENT YEARS?FIGURE 1Incremental Paid Loss Arraysition is essentially the same for other kinds of data. We assumethat the reader is familiar with the usual triangular developmentlayout.Consider the incremental array P =[p ij ], i =1,:::,s; j =0,:::,s ¡ 1; i + j · s (the array of incremental payments–the actualamounts paid in each development year in respect of eachaccident year–contains the fundamental observed quantities).The chain ladder is usually presented in something like thefollowing fashion. Let us take an array of paid losses (incrementalamounts paid), p ij , and cumulate along the accidentyears, c ij = p i0 + p i1 + ¢¢¢+ p ij ,sothatc ij = P jk=0 p ik are the correspondingcumulative paid loss amounts. Then compute ratiosr j = P i c ij =P i c i,j¡1 , where the sum is over all available termsthat are present in both the jth and (j ¡ 1)th columns. Forecastsare produced by projecting elements on the last diagonal c i,s¡ito the next development by multiplying by the development ra-