A Tweedie Compound Poisson Model in Reproducing Kernel Hilbert Space

Abstract

Tweedie models can be used to analyze nonnegative continuous data with a probability mass at zero. There have been wide applications in natural science, healthcare research, actuarial science, and other fields. The performance of existing Tweedie models can be limited on today’s complex data problems with challenging characteristics such as nonlinear effects, high-order interactions, high-dimensionality and sparsity. In this article, we propose a kernel Tweedie model, Ktweedie, and its sparse variant, SKtweedie, that can simultaneously address the above challenges. Specifically, nonlinear effects and high-order interactions can be flexibly represented through a wide range of kernel functions, which is fully learned from the data; In addition, while the Ktweedie can handle high-dimensional data, the SKtweedie with integrated variable selection can further improve the interpretability. We perform extensive simulation studies to justify the prediction and variable selection accuracy of our method, and demonstrate the applications in ratemaking and loss-reserving in general insurance. Overall, the Ktweedie and SKtweedie outperform existing Tweedie models when there exist nonlinear effects and high-order interactions, particularly when the dimensionality is high relative to the sample size. The model is implemented in an efficient and user-friendly R package ktweedie (https://cran.r-project.org/package=ktweedie).

Keywords:

• Insurance claims data
• Loss-reserving
• Ratemaking
• Sparse kernel methods
• Zero inflated data

Supplementary Materials

Supplementary Material includes derivations, proofs, Algorithms S1–S3, Tables S1–S4, and Figures S1–S10 in Sections A–F, as well as R code to reproduce Simulation Case I and links to the development and CRAN versions of the R package ktweedie.

Acknowledgments

We sincerely thank the Editor, the Associate Editor, and two anonymous Reviewers for their valuable comments toward improving this work.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

Yi Lian acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) PGSD2-519554-2018. Archer Yi Yang acknowledges the support of the NSERC Discovery grant RGPIN-2016-05174.