Risk and return of reinsurance contracts under copula models

Abstract

The aim of this article is to study the influence of nonlinear dependencies on the payoff of reinsurance contracts and the resulting effects on a non-life insurer's risk and return profile. To achieve this, we integrate several copula models and reinsurance contracts in a dynamic financial analysis framework and conduct numerical tests within a simulation study. Depending on the reinsurance contract and the copula concept employed, we find large differences in risk assessment for the ruin probability and for the expected policyholder deficit. This has important implications for management decisions, as well as for regulators and rating agencies that use these risk measures for deriving capital standards and ratings.

Keywords:

• enterprise risk management
• asset liability management
• dynamic risk modeling
• dynamic financial analysis
• solvency analysis
• reinsurance
• performance measurement
• simulation
• copulas

Acknowledgements

The authors are grateful to Charles D. Cowan, Nadine Gatzert, Michael Luhnen, Andrea Macarina, Thomas Parnitzke, Hato Schmeiser, and the participants of the European Journal of Finance and Warwick Business School Conference on Copulae and Multivariate Probability Distributions in Finance for valuable suggestions and comments.