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

ARCHITECTURE FOR RESIDENTIAL PROPERTY INSURANCE RATEMAKING 533Why accumulate? Theoretically, the key factor represents theloss cost at a given (incremental) TVI range relative to the losscost at the base value, but the loss cost series for individual TVIranges is simply too volatile to use directly. Instead, use the morestable cumulative loss cost series to mark selected cumulativeloss costs at “target” points (generally every $25,000 of TVI),and calculate the implied incremental loss cost in the target rangeby decomposing the cumulative value as follows.The known cumulative losses can be represented as the sumof a series of incremental loss costs times incremental exposurein each TVI range up to the current one:where:L k = ¯¸k ¯Wk = ¸1W 1 + ¢¢¢+ ¸kW k¸i = the incremental loss cost in each range (i =1,2,:::,k);W i = the exposure weight in each range;and bars above indicate cumulative totals for ranges “up through”an amount. Then solve for the incremental loss cost for the currentrange (denoted by k) from the cumulative totals and theexposure in the current range:¯¸k ¯Wk ¡ ¯¸(k¡1)¯W(k¡1)¸k =: (14)W kOnce the implied key factors are found for each of the targetranges, interpolate linearly between every two target points tofind the key factor for the $5,000 ranges in between.When selecting cumulative loss costs at target points, onemust be careful to keep the implied marginal key factor (differencebetween key factors for successive $5,000 ranges) betweenthe theoretical lower and upper bounds of:² Zero (meaning no additional losses are expected despite theincrease in policy limit), and