Manually Adjustable Link Ratio Model for Reserving

The chain ladder method is very popular in General/Property-Casualty Insurance actuarial circles. Mack [1] expanded the deterministic algorithm to include calculations for the variance of the chain ladder projections. The assumptions underlying the chain ladder method are important in regards to the appropriateness of the deterministic projections; they are even more important in regards to the appropriateness of the stochastic results. The purpose of this paper is to introduce more statistical rigor to this popular method and help close the link between practice and statistical theory. We will discuss residual analysis and other statistical measures as they apply to the chain ladder method so that the appropriateness of its deterministic and stochastic results can be objectively measured based on statistically rigorous principles. We will also show how the regression approach of Murphy [2] can be expanded so that link ratios “selected judgmentally” can be seen as conforming to an underlying statistical model.

Keywords: chain ladder; selection; residuals; Mack; Murphy