Regression Shrinkage and Selection for Actuarial Models

This paper demonstrates an approach to apply the lasso variable shrinkage and selection method to loss models arising in actuarial science. Specifically, the group lasso penalty is applied to the GB2 distribution, which is a popular distribution used often in actuarial research nowadays. The paper illustrates how the majorization minimization principle can be used to construct a fast and stable algorithm to estimate the coefficients for the regression model with shrinkage and selection. The shape parameters for the GB2 distribution are automatically estimated by the routine. The new regression routine is called HDGB2. In the simulation section of the paper, the HDGB2 routine is compared with the log-normal GLMNET routine, so as to demonstrate that HDGB2 results in a better fit of the data when the underlying true severity distribution is a GB2 distribution. In the empirical study of the paper, the HDGB2 routine is used to estimate the coefficients for a GB2 indemnity amounts model for the U.S. crop insurance data obtained from the Risk Management Agencey (RMA). For the Michigan subset of the data, we are able to discover that HDGB2 results in a better distributional fit than the log-normal GLMNET routine, in the out-of-sample