Flexible Factor Chain Ladder Model: A Stochastic Framework for Reasonable Link Ratio Selections

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.

Keywords: chain ladder; selection; Mack; Murphy; variance; reserve risk; residuals