Reinsurance contract design with adverse selection

ABSTRACT

In light of the richness of their structures in connection with practical implementation, we follow the seminal works in economics to use the principal–agent (multidimensional screening) models to study a monopolistic reinsurance market with adverse selection; instead of adopting the classical expected utility paradigm, the novelty of our present work is to model the risk assessment of each insurer (agent) by his value-at-risk at his own chosen risk tolerance level consistent with Solvency II. Under information asymmetry, the reinsurer (principal) aims to maximize his average profit by designing an optimal policy provision (menu) of ‘shirt-fit’ reinsurance contracts for every insurer from one of the two groups with hidden characteristics. Our results show that a quota-share component, on the top of simple stop-loss, is very crucial for mitigating asymmetric information from the insurers to the reinsurer.

KEYWORDS:

• Reinsurance
• principal–agent problem
• value-at-risk
• combination of deductible and quota-share

Acknowledgments

The authors would like to thank the referee for useful suggestions and comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Ka Chun Cheung acknowledges the financial support of the Research Grants Council of HKSAR, University Grants Committee (GRF Project 17324516). The second author Phillip Yam acknowledges the financial support from The Hong Kong RGC GRF 14301015 with the project title: Advance in Mean Field Theory and The Hong Kong RGC GRF 14300717 with the project title: New kinds of forward-backward stochastic systems with applications, and the financial support from the Faculty of Science of Chinese University of Hong Kong via the CUHK Direct Grants with internal code numbers: 3132761 and 3132762. Phillip Yam also acknowledges the financial support from Department of Statistics of Columbia University in the City of New York during the period he was a visiting faculty member. The third author Kevin Yuen acknowledges that this work is supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. UGC/FDS14/P02/16).