We want to present a machine learning application in life insurance. We are analyzing lapse rates using data from an international life insurance company. An adequate lapse model is crucial to manage the assets and liabilities and to fulfil solvency requirements.

We propose an extended LASSO approach. Depending on the structure of a covariable, we use different subpenalties to model the different covariables. We distinguish between regular LASSO, fused LASSO and trend filtering. By that we are able to find the main trends of the data set and even find trends within the covariables. The model is multivariate, automated and interpretable. Due to the regularization there is little risk of overfitting the data and we can control the bias variance tradeoff with the hyperparameter lambda.

We show both the theoretical framework of the model and the application with real world data. We also discuss the advantages of the model and compare it to other models like a univariate Whittaker Henderson approach or a GLM.