Bayesian CART models for aggregate claim modeling

ArXiv ID: 2409.01908 “View on arXiv”

Authors: Unknown

Abstract

This paper proposes three types of Bayesian CART (or BCART) models for aggregate claim amount, namely, frequency-severity models, sequential models and joint models. We propose a general framework for the BCART models applicable to data with multivariate responses, which is particularly useful for the joint BCART models with a bivariate response: the number of claims and aggregate claim amount. To facilitate frequency-severity modeling, we investigate BCART models for the right-skewed and heavy-tailed claim severity data by using various distributions. We discover that the Weibull distribution is superior to gamma and lognormal distributions, due to its ability to capture different tail characteristics in tree models. Additionally, we find that sequential BCART models and joint BCART models, which incorporate dependence between the number of claims and average severity, are beneficial and thus preferable to the frequency-severity BCART models in which independence is assumed. The effectiveness of these models’ performance is illustrated by carefully designed simulations and real insurance data.

Keywords: Bayesian CART, frequency-severity models, claim amount modeling, Weibull distribution, bivariate response, Insurance

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail
• Why: The paper introduces advanced Bayesian CART models with multivariate responses and specialized distributions (e.g., Weibull, compound Poisson gamma), requiring sophisticated probability theory and computation. It validates these models through both carefully designed simulations and real insurance data analysis, demonstrating a strong empirical foundation for practical implementation.

  flowchart TD
    Start["Research Goal:<br/>Propose Bayesian CART models<br/>for aggregate claim modeling"] --> Inputs["Data & Inputs:<br/>Simulated & Real Insurance Data<br/>(Count, Severity, Aggregate)"]

    Inputs --> Methodology["Methodology:<br/>Develop 3 Bayesian CART Frameworks:<br/>1. Frequency-Severity<br/>2. Sequential<br/>3. Joint (Bivariate)"]

    Methodology --> Computation["Computational Process:<br/>MCMC Sampling<br/>(Gibbs & Metropolis-Hastings)<br/>Tree Structure Learning"]

    Computation --> Analysis["Model Analysis:<br/>Compare Distributions:<br/>Weibull vs. Gamma vs. Lognormal<br/>Test Independence Assumptions"]

    Analysis --> Outcomes["Key Findings & Outcomes:<br/>1. Weibull best for heavy-tailed severity<br/>2. Joint/Sequential models outperform<br/>   Frequency-Severity (due to dependence)<br/>3. Effective for multivariate responses"]