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On optimal reinsurance in the presence of premium budget constraint and reinsurer’s risk limit

Published online by Cambridge University Press:  20 March 2024

Wei Liu  and
Yijun Hu
Wei Liu*
Affiliation:
Xinjiang University
Yijun Hu*
Affiliation:
Wuhan University
*
*Postal address: College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, 830046, People’s Republic of China. Email address: liuwei_math@sina.com
**Postal address: School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, 430072, People’s Republic of China. Email address: yjhu.math@whu.edu.cn
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Abstract

In this paper, we propose two new optimal reinsurance models in which both premium budget constraints and the reinsurer’s risk limits are taken into account. To be precise, we assume that the reinsurance premium has an upper bound, and that the admissible ceded loss functions have a pre-specified upper limit. Moreover, we assume that the reinsurance premium principle is calculated by the expected value premium principle. Under the optimality criteria of minimizing the value at risk and conditional value at risk of the insurer’s total risk exposure, we derive the explicit optimal reinsurance treaties, which are layer reinsurance treaties. A new approach is developed to construct the optimal reinsurance treaties. Comparisons with existing studies are also made. Finally, we provide a numerical study based on real data and an example to illustrate the proposed models and results. Our work provides a novel generalization of several known achievements in the literature.

Keywords

Optimal reinsurancebudget constraintvalue at riskconditional value at riskexpected value premium principle
Type
Original Article
Information
Advances in Applied Probability , First View , pp. 1 - 28
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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