A Family of Chain-Ladder Factor Models for Selected Link Ratios

The models of Mack (1993) and Murphy (1994) are expanded to a continuously indexed family of chain-ladder models by broadening the variance structure of the error term. It is shown that, subject to certain restrictions, an actuary’s selected report-to-report factor can be considered the best linear unbiased estimate for some member of this family. The approach given in Murphy (1994) yields a mean square error estimate of the unpaid claim liability that is consistent with the actuary’s selections.