Modeling dependence in sparse time series of Insurance Claims

2026-05-25

AI Summary

This study addresses the challenge of modeling dependence among multiple insurance risk classes, particularly under sparse claim time series where traditional Lévy copula and zero-inflated mixture models suffer from difficulties in simulation and parameter calibration. To overcome these limitations, the authors propose the Comb-Bernoulli model, which innovatively integrates the strengths of copula-based dependence structures with sparse-event modeling. The framework supports joint modeling using a Gaussian copula and log-normal marginal distributions, ensuring theoretical rigor while enabling efficient likelihood evaluation, parameter estimation, and numerical simulation. Empirical evaluation on the Danish fire insurance dataset demonstrates that the proposed model significantly outperforms conventional approaches, achieving superior performance in both modeling accuracy and computational efficiency for practical risk management applications.

Abstract

Modeling the dependence between multiple risk types is a central challenge in contemporary insurance risk management. The standard approaches, Lévy copulas and zero-mixed models, often face practical difficulties in simulation and parameter calibration. In this paper, we introduce the Comb-Bernoulli model, a novel framework for capturing dependence between sparse time series of insurance risks, bridging the benefits of the two standard approaches. The (traditional) copula structure of the proposed model enables tractable: i) simulation, ii) likelihood evaluation, and iii) estimation of dependence parameters. We present the general properties of the model and analyze in detail the Gaussian copula case with lognormal marginals. Moreover, we illustrate an application using the Danish fire insurance dataset, highlighting both the modeling strengths and numerical efficiency of our approach in real-world risk management.

Problem

• dependence modeling
• sparse time series
• insurance claims
• risk management
• multivariate risk

Innovation

• Comb-Bernoulli model
• sparse time series
• insurance risk dependence
• copula
• parameter estimation