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OPTIMAL REINSURANCE FROM THE VIEWPOINTS OF BOTH AN INSURER AND A REINSURER UNDER THE CVAR RISK MEASURE AND VAJDA CONDITION

Published online by Cambridge University Press:  12 April 2021

Yanhong Chen
Yanhong Chen*
Affiliation:
College of Finance and Statistics Hunan UniversityChangsha, Hunan410082People’s Republic of China E-Mail: yhchen@hnu.edu.cn
*
E-Mail: yhchen@hnu.edu.cn
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Abstract

In this paper, we study the optimal reinsurance contracts that minimize the convex combination of the Conditional Value-at-Risk (CVaR) of the insurer’s loss and the reinsurer’s loss over the class of ceded loss functions such that the retained loss function is increasing and the ceded loss function satisfies Vajda condition. Among a general class of reinsurance premium principles that satisfy the properties of risk loading and convex order preserving, the optimal solutions are obtained. Our results show that the optimal ceded loss functions are in the form of five interconnected segments for general reinsurance premium principles, and they can be further simplified to four interconnected segments if more properties are added to reinsurance premium principles. Finally, we derive optimal parameters for the expected value premium principle and give a numerical study to analyze the impact of the weighting factor on the optimal reinsurance.

Keywords

Optimal reinsurancerisk measureConditional Value-at-RiskVajda condition91B3091B3291B70
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 2 , May 2021 , pp. 631 - 659
Copyright
© 2021 by Astin Bulletin. All rights reserved

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Footnotes

*

Supported by the National Natural Science Foundation of China (No. 11901184) and the Natural Science Foundation of Hunan Province (No. 2020JJ5025).

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