Speaker(s): Katrien Antonio (KU Leuven)
Insurance companies use predictive models for a variety of analytic tasks, including pricing, marketing campaigns, claims handling, fraud detection and reserving. Typically, these predictive models use a selection of continuous, ordinal, nominal and spatial risk factors to differentiate risks. Such models should not only be competitive, but also interpretable by stakeholders (including the policyholder and the regulator) and easy to implement and maintain in a production environment. That is why current actuarial literature puts focus on generalized linear models where risk cells are constructed by binning risk factors up front, using ad hoc techniques or professional expertise. In statistical literature penalized regression is often used to encourage the selection and fusion of predictors in predictive modeling. Most penalization strategies work for data where predictors are of the same type, such as LASSO for continuous variables and Fused LASSO for ordered variables. We design an estimation strategy for generalized linear models which includes variable selection and the binning of risk factors through L1-type penalties. We consider the joint presence of different types of covariates and a specific penalty for each type of predictor. Using the theory of proximal operators, our estimation procedure is computationally efficient since it splits the overall optimization problem into easier to solve sub-problems per predictor and its associated penalty. As such, we are able to simultaneously select, estimate and group, in a statistically sound way, any combination of continuous, ordinal, nominal and spatial risk factors.
We illustrate the approach with simulation studies, an analysis of Munich rent data, and a case-study on motor insurance pricing.
This presentation will cover ongoing work by Sander Devriendt, Katrien Antonio, Edward (Jed) Frees and Roel Verbelen.