Regularized Regression for Reserving and Mortality Models

Abstract

Bayesian regularization, a relatively new method for estimating model parameters, shrinks estimates towards the overall mean by shrinking the parameters. It has been proven to lower estimation and prediction variances from those of MLE for linear models, such as regression or GLM. It has a goodness-of-fit measure, and can readily be applied using available software. This can be used for any type of actuarial linear modeling, but it is slightly more complicated for mortality and loss reserving models that use row, column, and diagonal effects for array data. These are called age-period-cohort, or APC models by statisticians. The problem is that the row, column and diagonal effects are not what should be shrunk. These models can easily become over-parameterized, and actuaries often reduce parameters with smooth curves or cubic splines. We discuss an alternative smoothing method that uses regularization, with its reduction in estimation errors, and illustrate both its classical and Bayesian forms and their application to APC modeling. Typical actuarial models and some generalizations are used as examples.