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Operations Research Transactions >

2019 , Vol. 23 >Issue 4: 13 - 33

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2019.04.002

The optimal reinsurance problem towards joint interests of the insurer and the reinsurer with dependent risks

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  • 1. School of Business, Hunan Normal University, Changsha 410081, China;
    2. Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China

Received date: 2017-11-29

  Online published: 2019-12-04

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Abstract

In this paper, by considering the joint interests of the insurer and the reinsurer, we study the optimal reinsurance problem in a risk model with two dependent classes of insurance business. Assume that the reinsurance company adopts the variance premium principle. The surplus processes of the insurance company and the reinsurance company are both governed by the compound Poisson model as well as by the diffusion approximation model. Under the criterion of maximizing the expected utility, we prove the existence and uniqueness of the optimal reinsurance strategies. By solving the corresponding Hamilton-Jacobi-Bellman equations, closed-form expressions for the optimal reinsurance strategies and the value functions are derived for the two models. Moreover, we also present numerical examples and analysis.

Key words： surplus process; reinsurance; variance premium principle; dependent claims; expected utility

Cite this article

HUAGN Ya, WANG Jing, ZHOU Jieming, DENG Yingchun . The optimal reinsurance problem towards joint interests of the insurer and the reinsurer with dependent risks[J]. Operations Research Transactions, 2019 , 23(4) : 13 -33 . DOI: 10.15960/j.cnki.issn.1007-6093.2019.04.002

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