# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2020103

## Optimal reinsurance with default risk: A reinsurer's perspective

 1 School of Mathematics and System Sciences, Xinjiang University, Urumqi Xinjiang, 830046, China 2 School of Mathematics and Statistics, Wuhan University, Wuhan Hubei, 430072, China

* Corresponding author: Lijun Wu

Received  May 2019 Revised  January 2020 Published  June 2020

Fund Project: This work was supported by the National Natural Science Foundation of China (Nos: 11601463, 11861064, 11771343)

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.

Citation: Tao Chen, Wei Liu, Tao Tan, Lijun Wu, Yijun Hu. Optimal reinsurance with default risk: A reinsurer's perspective. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020103
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