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

WHEN CAN ACCIDENT YEARS BE REGARDED AS DEVELOPMENT YEARS? 247the classical chain ladder forecasts and that models that don’t doso should not be referred to as chain ladder models.Murphy [7] explicitly writes several loss development factormethods as stochastic models and derives forecast variances,working in a least-squares framework. He argues that it is oftennecessary to extend ratio models to include intercepts.Barnett and Zehnwirth [1] develop a statistical framework extendingMurphy’s approach to include some adjustment for commonaccident and calendar period trends as a general diagnostictool for testing the suitability of ratio models to data. Multipleexamples point toward some common deficiencies of ratio models,including the need for an intercept and the lack of predictivepower of ratios after incorporating obvious predictors.Renshaw and Verrall [8] derive another model that reproducesthe chain ladder. Their formulation makes the number of parametersdescribing the mean process in the chain ladder explicit.The model is initially presented as a Poisson model, which extendsto a quasi-likelihood framework as a model with varianceproportional to the mean.Even though we started with a form of the chain ladder thatlooked something like the stochastic form presented by Mack[5, 6] and Murphy [7], by the end of Section 2 there are strongsimilarities to the stochastic form presented by Renshaw and Verrall[8]. Despite arguments in the literature, the two approachesdiffer mainly in the data on which they appear to condition whendescribing the past, and in the number of variance parametersthey employ. They are identical in the way they describe the meanpredictions for the future, which is why they both reproduce thechain ladder forecasts. Given a quasi-likelihood approach, differencesin forecast standard errors appear to be largely due to twofactors–the number of variance parameters, and the number ofdegrees of freedom to fit the data (i.e., parameters) for which theparameter uncertainty is ignored.