Optimal reinsurance with default risk: A reinsurer's perspective

Abstract

In this paper, we study the optimal reinsurance design with default risk by minimizing the VaR (value at risk) of the reinsurer's total risk exposure. The optimal reinsurance treaty is provided. When the reinsurance premium principle is specified to the expected value and exponential premium principles, the explicit expressions for the optimal reinsurance treaties are given, respectively.2020 Mathematics Subject Classification. 91B30. Key words and phrases. Optimal reinsurance, default risk, value at risk, expected value premium principle, exponential premium principle.