Probabilistic Framework for Evaluating Materiality and Variability in Loss Reserve Estimates

A reserve point estimate is usually presented without explicit quantitative reference to the variability associated with it. The literature provides little guidance on how to go about providing such quantitative representations. In this paper the authors present a new function, called the coefficient of estimation, as a measure of the placement of a reserve point estimate on the continuum of reserve estimates defined by the underlying aggregate loss distribution. The authors further use this coefficient to discuss six commonly used reserving terms to illustrate how the variability inherent in a point reserve estimate may be quantified. The authors also illustrate these ideas with six different demonstrations for each of two lines of business, including tables and charts depicting underlying aggregate loss distributions. The authors conclude the paper with a series of observations to amplify some of the salient issues as well as set some boundaries for the usefulness of the proposed coefficient of estimation.