Document Type : Original Research Paper

Authors

• M. Mirbgherijam ¹
• M.N. Shahiki Tash ¹
• Gh. Zamanian ¹
• A. Safari ²

¹ Department of Economic Sciences, Faculty of Management and Economics, University of Sistan and Baluchestan, Zahedan, Iran

² Department of Insurance Research Institute, Tehran, Iran

Abstract

In this research, underwriting risks of insurance industry aggregated with two different approaches; they are simultaneous aggregation with elliptical copulas and Archimedean copulas and hierarchical aggregation with Hierarchical Archimedean Copulas (HAC). And thus the required capital for insurance industry has been determined. Obtained results in the modeling dependency structure and aggregation of the underwriting risks using the data of loss ratio during 1975-2013 shows that, due to the different type of dependency structures of underwriting risks, the estimation of the minimum capital required across different approaches and copulas used are different from each other. Calculation of solvency required capital under the standard model of Directive No. 69 of Central Insurance Company to cover underwriting risks of insurance industry is 96,943,391 million Rials, using real data of the year 2013.However, estimated required capital with the risk measure VaR at 95% level of confidence is less than this amount, using elliptical copulas at first approach and using Clayton and Joey copulas at both approaches. Thus one  may conclude that using these types of copulas to determine the required capital of insurance firms leads to overestimating the solvency of firms compared to what is estimated using standard simple and linear aggregation methods models.

Keywords

• Copulas
• Dependency structur
• Hierarchical archimedean copulas
• Insurance
• Risk aggregation
• Underwriting risk