Optimal reinsurance designs based on risk measures: a review

Abstract

Reinsurance is an effective way for an insurance company to control its risk. How to design an optimal reinsurance contract is not only a key topic in actuarial science, but also an interesting research question in mathematics and statistics. Optimal reinsurance design problems can be proposed from different perspectives. Risk measures as tools of quantitative risk management have been extensively used in insurance and finance. Optimal reinsurance designs based on risk measures have been widely studied in the literature of insurance and become an active research topic. Different research approaches have been developed and many interesting results have been obtained in this area. These approaches and results have potential applications in future research. In this article, we review the recent advances in optimal reinsurance designs based on risk measures in static models and discuss some interesting problems on this topic for future research.

Keywords

• value-at-risk
• conditional value-at-risk
• distortion risk measures
• layer reinsurance
• optimal reinsurance designs