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Optimal allocation of policy limits in layer reinsurance treaties

Part of: Special processes Distribution theory - Probability Operations research and management science

Published online by Cambridge University Press:  24 November 2022

Chuchu Wang ,
Wei Wang ,
Yiying Zhang Open the ORCID record for Yiying Zhang [Opens in a new window]  and
Peng Zhao Open the ORCID record for Peng Zhao [Opens in a new window]
Chuchu Wang
Affiliation:
School of Mathematics and Statistics, Jiangsu Provincial Key Laboratory of Educational Big Data Science and Engineering, Jiangsu Normal University, Xuzhou 221116, P.R. China
Wei Wang
Affiliation:
School of Mathematics and Statistics, Jiangsu Provincial Key Laboratory of Educational Big Data Science and Engineering, Jiangsu Normal University, Xuzhou 221116, P.R. China
Yiying Zhang
Affiliation:
Department of Mathematics, Southern University of Science and Technology, Shenzhen 518055, P.R. China. E-mail: zhangyy3@sustech.edu.cn
Peng Zhao
Affiliation:
School of Mathematics and Statistics, Jiangsu Provincial Key Laboratory of Educational Big Data Science and Engineering, Jiangsu Normal University, Xuzhou 221116, P.R. China
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Abstract

Layer reinsurance treaty is a common form obtained in the problem of optimal reinsurance design. In this paper, we study allocations of policy limits in layer reinsurance treaties with dependent risks. We investigate the effects of orderings and heterogeneity among policy limits on the expected utility functions of the terminal wealth from the viewpoint of risk-averse insurers faced with right tail weakly stochastic arrangement increasing losses. Orderings on optimal allocations are presented for normal layer reinsurance contracts under certain conditions. Parallel studies are also conducted for randomized layer reinsurance contracts. As a special case, the worst allocations of policy limits are also identified when the exact dependence structure among the losses is unknown. Numerical examples are presented to shed light on the theoretical findings.

Keywords

ComonotonicityLayer reinsurance treatyMajorizationRWSAIStop-loss order

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60E15: Inequalities; stochastic orderings 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Special Issue 2: Probability and stochastic modeling in actuarial science and related fields , April 2023 , pp. 546 - 566
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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