Modeling insurance claims using Bayesian nonparametric regression.

Area of Science:

• Actuarial science
• Statistical modeling
• Risk management

Background:

• Parametric regression models are standard for predicting insurance claims but lack flexibility for complex, individual-level data.
• Insurance claims data often exhibit multimodal, skewed, and heavy-tailed distributions, challenging traditional models.
• Accurate prediction of claims frequency and severity is crucial for setting insurance premiums.

Purpose of the Study:

• To explore the application of Bayesian nonparametric (BNP) regression models for predicting insurance claims frequency and severity.
• To assess the predictive performance of BNP models against traditional parametric approaches using real-world insurance data.

Main Methods:

• Modeling claims frequency using a mixture of Poisson regression and claims severity using a mixture of normal regression.
• Employing Dirichlet process (DP) and Pitman-Yor process (PY) priors for regression parameters in a Bayesian nonparametric framework.
• Utilizing Markov chain Monte Carlo (MCMC) methods for model fitting and parameter estimation.

Main Results:

• BNP models demonstrated substantial reductions in mean squared error for claims frequency (52% and 33%) and severity (45% and 79%) on French and Belgian datasets.
• The flexibility of BNP models allows for individual-level parameter estimation, capturing complex data relationships.
• Significant improvements in prediction accuracy were observed compared to standard Poisson and multiple linear regression.

Conclusions:

• Bayesian nonparametric regression models provide a highly flexible and accurate alternative to parametric models for insurance claims prediction.
• The proposed BNP approach effectively handles the complexities of insurance claims data, leading to enhanced actuarial modeling.
• These findings support the adoption of BNP methods for more precise premium setting and risk assessment in the insurance industry.