Negative binomial models for development triangles of counts

2026-01-09

AI Summary

This study addresses the challenge of overdispersion commonly observed in insurance claim count data, which traditional models often fail to capture accurately. The authors propose a fully parametric model based on the negative binomial distribution, systematically applied for the first time to modeling development triangle count data. The approach initially assumes independence among random variables and is subsequently extended to incorporate dependence structures across different development years, while preserving negative binomial marginal distributions in both settings. Bayesian inference is employed for parameter estimation. Empirical evaluations on both simulated and real-world datasets demonstrate that the proposed method effectively accommodates overdispersion and significantly improves the accuracy of outstanding claim count predictions.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Prediction of outstanding claims has been done via nonparametric models (chain ladder), semiparametric models (overdispersed poisson) or fully parametric models. In this paper, we propose models based on negative binomial distributions for the prediction of outstanding number of claims, which are particularly useful to account for overdispersion. We first assume independence of random variables and introduce appropriate notation. Later, we generalise the model to account for dependence across development years. In both cases, the marginal distributions are negative binomials. We study the properties of the models and carry out bayesian inference. We illustrate the performance of the models with simulated and real datasets.

Problem

• negative binomial
• overdispersion
• outstanding claims
• development triangles
• claim counts

Innovation

• negative binomial
• overdispersion
• Bayesian inference
• development triangles
• claims prediction