A size-of-loss model for the negatively skewed insurance claims data: applications, risk analysis using different methods and statistical forecasting

Abstract

The future values of the expected claims are very important for the insurance companies for avoiding the big losses under uncertainty which may be produced from future claims. In this paper, we define a new size-of-loss distribution for the negatively skewed insurance claims data. Four key risk indicators are defined and analyzed under four estimation methods: maximum likelihood, ordinary least squares, weighted least squares, and Anderson Darling. The insurance claims data are modeled using many competitive models and comprehensive comparison is performed under nine statistical tests. The autoregressive model is proposed to analyze the insurance claims data and estimate the future values of the expected claims. The value-at-risk estimation and the peaks-over random threshold mean-of-order-p methodology are considered.

Keywords:

• Autoregressive model
• claims payment
• Cullen and Frey plot
• mean-of-order-p
• peaks-over random threshold
• risk analysis

Mathematics Subject Classifications:

• 60E05
• 62H05
• 62E10
• 62F10
• 62F15
• 62P05

Acknowledgments

The authors gratefully acknowledge with thanks the very thoughtful and constructive comments and suggestions of the Editor-in-Chief and the reviewers which resulted in much improved paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.