Paper: arXiv 2303.01923

Authors: Yaojun Zhang, Lanpeng Ji, Georgios Aivaliotis, Charles Taylor

Abstract

Accuracy and interpretability of a (non-life) insurance pricing model are essential qualities to ensure fair and transparent premiums for policy-holders, that reflect their risk. In recent years, the classification and regression trees (CARTs) and their ensembles have gained popularity in the actuarial literature, since they offer good prediction performance and are relatively easily interpretable. In this paper, we introduce Bayesian CART models for insurance pricing, with a particular focus on claims frequency modelling. Additionally to the common Poisson and negative binomial (NB) distributions used for claims frequency, we implement Bayesian CART for the zero-inflated Poisson (ZIP) distribution to address the difficulty arising from the imbalanced insurance claims data. To this end, we introduce a general MCMC algorithm using data augmentation methods for posterior tree exploration. We also introduce the deviance information criterion (DIC) for the tree model selection. The proposed models are able to identify trees which can better classify the policy-holders into risk groups. Some simulations and real insurance data will be discussed to illustrate the applicability of these models.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a solid Bayesian CART framework extended to zero-inflated Poisson distributions using MCMC and data augmentation. It effectively addresses insurance claim frequency imbalancement, supported by simulated and real actuarial data, balancing moderate mathematical density with practical empirical application.

Research Flowchart

  flowchart TD
    A[Goal: Accurate & Interpretable Insurance Claims Frequency Models] --> B[Input Data: Imbalanced Claims Data - Poisson, NB, ZIP]
    B --> C[Method: Implement Bayesian CART for Claims Frequency]
    C --> D[Computation: MCMC Algorithm with Data Augmentation]
    D --> E[Model Selection: Evaluate Trees using DIC]
    E --> F[Validation: Test on Simulated & Real Insurance Datasets]
    F --> G[Outcome: Superior Risk Group Classification & Fair Pricing]