Many practitioners are now using probabilistic versions of standard actuarial techniques, sometimes employing quite sophisticated tools in their estimation. However, none of these developments avoid the need for stringent checking of the suitability of model assumptions, a necessity that is often overlooked.
We discuss some of the statistical models underlying a variety of standard methods, construct a number of diagnostics for model assessment for several models and discuss how the underlying ideas carry over to many other methods for the estimation of liabilities. These tools are easy to implement and use. They allow practitioners to use the corresponding models with greater confidence, and gain additional information about the triangle. This information can have important consequences for the insurer.
We illustrate that some popular approaches—the Mack chain ladder, the quasi-Poisson GLM—and consequently predictions based on them (both bootstrapped and otherwise) have structure not present in real triangles, and don’t describe some features of the data. Consequently their associated intervals fail to have the desired properties.
We point out that many aspects of the reserving problem and the structure of real data lead us to model on the log scale. We briefly describe the Probabilistic Trend Family (PTF) models and its extension to the multivariate case (MPTF) and show that these model families can capture the patterns in real data and produce more reasonable prediction intervals.
