A Tweedie Compound Poisson Model in Reproducing Kernel Hilbert Space

• Activity Number: 474 - Emerging Methods and Applications in Insurance Data Science
• Type: Topic Contributed
• Date/Time: Wednesday, August 10, 2022 : 2:00 PM to 3:50 PM
• Sponsor: Casualty Actuarial Society
• Author(s): Yi Yang and Yi Lian and Boxiang Wang and Peng Shi and Robert William Platt*
• Companies: McGill University and McGill University and University of Iowa and University of Wisconsin-Madison and McGill University
• Keywords: Tweedie compound Poisson models; Reproducing kernel Hilbert space; Sparse kernel methods; Insurance claims data; Loss-reserving; Ratemaking

Abstract

Tweedie models can be used to handle non-negative 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 by today’s complex data problems with challenging characteristics such as high-dimensionality, nonlinear effects, high-order interactions. Motivated by these challenges, we propose a kernel Tweedie model with integrated variable selection. The non parametric nature of the the proposed method along with the abundance of available kernel functions provides much needed modeling flexibility and capability. The resulting sparsity due to the variable selection also improves the interpretability and the prediction accuracy. 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. The model is implemented in an efficient and user-friendly R package.