Chain Ladder Reserve Risk Estimators

Mack (1993) [2] and Murphy (1994) [4] derived analytic formulas for the reserve risk of the chain ladder method. In 1999, Mack [3] gave a recursive version of his formula for total risk. This paper provides the recursive versions of Mack’s formulas for process risk and parameter risk and shows that they agree with the formulas in Murphy [4] except for a parameter risk cross-product term. MSE is decomposed into variance and bias components. For the unbiased all-year weighted average link ratios in Mack [2] and Murphy [4] the MSE decomposition in this paper yields formulas that agree with Murphy [4]. For well-behaved triangles the difference between Mack and Murphy parameter risk estimates should be negligible. The concepts are illustrated with an example using data from Taylor and Ashe [5].