摘要：The popular General/Property-Casualty Insurance chain ladder method was first expanded to
include variance calculations by Mack [1]. As new research expands the chain ladder method’s stochastic
functionality, it is as important as ever to understand the assumptions underlying this fundamental
approach and evaluate their appropriateness given the data. The purpose of this paper is to introduce more
statistical rigor to this popular method and help bridge the gap between practice and statistical theory. We
will expand the regression approach of Murphy[2] so that selected link ratios other than simple or volume
weighted averages can be seen as optimizing a rigorous statistical model. We will derive formulas for the
parameter risk and process risk of ultimate losses projected from such selected link ratios. We will discuss
residual analysis and statistical measures for validating the selected factors. Using data previously analyzed
in the literature, we will compare stochastic results from the popular application of the Mack formula to
those based on our model. It is hoped that this paper will provide the actuarial practitioner with a
statistically rigorous framework with which to measure objectively the appropriateness of the chain ladder
deterministic and stochastic results, make more informed judgmental selections, and avoid injudicious
conclusions based on potentially inappropriate assumptions.
