Regularized Regression for Reserving and Mortality Models

Asia-Pacific Journal of Risk and Insurance

15 Pages Posted: 9 Aug 2018 Last revised: 27 Nov 2018

Date Written: July 24, 2018


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.

Keywords: Regularization, Bayesian Shrinkage, Age-Period-Cohort Models, Actuarial Modeling

JEL Classification: C11, C13, G22

Suggested Citation

Venter, Gary, Regularized Regression for Reserving and Mortality Models (July 24, 2018). Asia-Pacific Journal of Risk and Insurance . Available at SSRN: or

Gary Venter (Contact Author)

Columbia University ( email )

116th and Broadway
New York, NY 10027
United States

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