Modeling non-life insurance claims using Exponential Log-Logistics distribution

Abstract

Determining the amount of insurance claim in the insurance industry is a challenging task. This study aims at modelling and estimating loss claims from an insurance company, with a particular focus on extreme event risks. The main objective was to develop a distribution using the density hazard approach, characterized by skewness and heavy tail, to effectively capture both high-frequency small claims and low-frequency large claims. Various parametric distributions have been applied to the insurance loss claims to determine the model that best fits the data. The Exponential Log-Logistic distribution, characterized by parameters gives the best fit for the data, as indicated by the lowest negative log-likelihood (NLL) value. Comparative analysis highlights the Exponential Log-Logistic distribution’s superior performance in modeling heavy-tailed and skewed data, essential for accurate risk assessment in insurance. In contrast, the Log-Normal distribution, while achieving the lowest Bayesian Information Criterion (BIC) value does not fit the data as well in terms of NLL. The Value at Risk (VaR) and Expected Shortfall (ES) metrics further support the effectiveness of the proposed model in predicting risk management. The Exponential Log-Logistic distribution’s higher VaR values, and reasonably high ES values underscore its robustness in managing insurance risks. The findings recommend the Exponential Log-Logistic distribution as the most suitable model for insurance claims data, due to its balance of complexity and fit, offering significant improvements over simpler models like the Exponential and Lomax distributions. This model’s ability to accurately represent the distribution of claims supports better risk management and pricing strategies in the insurance industry.

Keywords Skewness, heavy-tailed, density hazard distribution, Insurance Claims, Parametric distributions.