Motivation The Hayne MLE family of models are quite elegant in their application, but like most models in order to address the needs of the practicing actuary the modeling framework needs to allow for the flexibility to deal with many different practical issues. While actuaries are accustomed to making practical adjustments to their algorithms, there is motivation to stay as close to the theoretical underpinnings of the models as possible in order to maintain a sound foundation. Whenever the paper strays a bit from the theory, those departures are noted so practitioners can adequately judge their impact.
Method This paper starts by reviewing the Hayne MLE modeling framework using a standard notation. Then it covers a number of practical data issues and addresses the diagnostic testing of the model assumptions. Next it will explore a variety of enhancements to the basic framework to allow the models to address other issues related to reserving and pricing risk. Finally, since no single model is perfect, ways to combine or credibility weight the Hayne MLE model results with various other models are explored in order to arrive at a “best estimate” of the distribution. This is similar to how a deterministic best estimate is generally derived in practice, so ways for the practitioner to correlate models by segment in order to simulate aggregate results are discussed.
Results The paper will illustrate the practical implementation of the Hayne MLE modeling framework as a powerful tool for estimating a distribution of unpaid claims.
Conclusions The paper outlines the full versatility of the Hayne MLE models for the practicing actuary.
Availability In lieu of technical appendices, several companion Excel workbooks are included that illustrate the calculations described in this paper.
Keywords Maximum Likelihood Estimate, Reserve Variability, Reserve Range, Distribution of Possible Outcomes, Generalized Linear Model, Best Estimate
