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

By Emmanuel Theodore Bardis, Ali Majidi, Daniel M. Murphy

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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.

KEYWORDS: Chain ladder, Mack, Murphy, variance, mean square error, reserve risk, regression

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Bardis, Emmanuel Theodore, Ali Majidi, and Daniel M. Murphy, "A Family of Chain-Ladder Factor Models for Selected Link Ratios," Variance 6:2, 2012, pp. 143-160.

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Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.