Adaptive splines for continuous features in risk assessment

Number and location of knots strongly impact on fitted values obtained from spline regression methods. P-splines have been proposed to solve this problem by adding a smoothness penalty to the log-likelihood. This paper aims to demonstrate the strong potential of A-splines (for adaptive splines) proposed by Goepp et al. (2018) for dealing with continuous risk features in insurance studies. Adaptive ridge is used to remove the un-necessary knots from a large number of candidate knots, yielding a sparse model with high interpretability. Two applications are proposed to illustrate the performances of A-splines. First, death probabilities are graduated in a Binomial regression model. Second, continuous risk factors are included in a Poisson regression model for claim counts in motor insurance. The move from technical to commercial price list can easily be achieved by switching to A-splines of degree 0, i.e. piecewize constant functions