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

242 WHEN CAN ACCIDENT YEARS BE REGARDED AS DEVELOPMENT YEARS?FIGURE 3Depiction of the Incrementals Involved in theCalculation of the Ratioc ij . Then the jth ratio is r j = A ij =A i,j¡1 . Note that A ij is alsothe sum of all the incremental loss amounts above the (i,j) cell(p kj , k =1,2,:::,i ¡ 1) plus all the incremental loss amounts tothe left of those. That is, A ij and A i,j¡1 are the sums of all theincremental loss amounts in the regions shown in Figure 3. If thevalues of the incrementals are represented by heights of squareprisms in each (i,j) cell, values represented by A, B and C inFigure 4, may be thought of as the “total volume” in the markedregions.Note further that (since the forecasts of the cumulative paidloss are in the same ratio) the formula r j = A ij =A i,j¡1 as a ratioof sums of incrementals as defined above applies to observationsin later (further into the future) calendar years as well, as long asany unobserved incremental loss amounts in the sum are replacedwith their predicted values.