Classical Partial Credibility with Application to Trend

Even with the recent advances in Bayesian credibility theory, there remain situations in which some may prefer the classical approach. Such situations may include data limitations, the failure of Bayesian model assumptions, the desire to incorporate a broader class of auxiliary information, ease of calculation and explanation, or just the force of tradition. This paper discusses a probabilistic interpretation of the classical square root rule which provides some rationale for its use. The same rationale applied to trend projections leads to a similar rule, which utilizes the relative goodness of fit of the trend line. While classical credibility for pure premiums is calculated from the volume of data used, the importance of volume is only in determining certain confidence intervals, which in turn determine credibility. In the trend model, the relative goodness of fit determines the confidence intervals. Using these confidence intervals in the same manner as in the pure premium case yields classical credibilities for the trend. Volume is important here only to the extent that the stability it imparts contributes to the goodness of fit. As there may be other influences affecting the fit, volume alone does not guarantee high credibility in the trend case. Credibility requirements under the Normal Power approximation also are reviewed. For these a partial credibility method different from the square root formula is indicated.