A practical support vector regression algorithm and kernel function for attritional general insurance loss estimation

Abstract

Abstract The aim of the paper is to derive a simple, implementable machine learning method for general insurance losses. An algorithm for learning a general insurance loss triangle is developed and justified. An argument is made for applying support vector regression (SVR) to this learning task (in order to facilitate transparency of the learning method as compared to more “black-box” methods such as deep neural networks), and SVR methodology derived is specifically applied to this learning task. A further argument for preserving the statistical features of the loss data in the SVR machine is made. A bespoke kernel function that preserves the statistical features of the loss data is derived from first principles and called the exponential dispersion family (EDF) kernel. Features of the EDF kernel are explored, and the kernel is applied to an insurance loss estimation exercise for homogeneous risk of three different insurers. Results of the cumulative losses and ultimate losses predicted by the EDF kernel are compared to losses predicted by the radial basis function kernel and the chain-ladder method. A backtest of the developed method is performed. A discussion of the results and their implications follows.