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

508 ARCHITECTURE FOR RESIDENTIAL PROPERTY INSURANCE RATEMAKINGexpenses is in the policy expense fee, using:E = f £ ¯P (9)where ¯P is the average premium per policy from experience data.The decomposition of fair premium may affect rating factorsas well, depending upon actuarial assumptions. Class rating factorsby peril are derived from class loss cost relativities, whichin turn are determined from experience data or model output.Assume a loss cost relativity is ®, so that the class loss cost is:X 0 = ®X:If fixed reinsurance costs are included in the base rate and notincreased or reduced in proportion to the expected loss cost forthe class, then the indicated class rate is:B 0 = X0 + F R1 ¡ vper formula (7). Substituting for X 0 , the ratio of the class to baserate (a.k.a. the correct class factor) is:½ = B0B = ®X + F R(10)X + F Ras the variable expense ratio cancels out of the quotient.Note that in cases where:1. One chooses not to recover a portion of fixed reinsurancecosts in the base rate for the peril, or;2. One assumes that fixed reinsurance costs allocated to theclass vary in proportion to class loss costs;the formula reduces to ® and the loss cost relativity is the correctpremium relativity. Though non-loss reinsurance costs wereassumed “fixed” for the overall rate level calculation, the assumptionabout whether they should be treated as fixed by class