扩散风险模型下再保险策略选择博弈研究
摘要
作为维持保险公司正常经营的重要手段，再保险是指保险人在原保险合同
的基础上，通过签订分保合同，将其所承保的部分风险和责任向其他保险人进
行保险的行为。再保险合约双方作为两个不同的主体，对于再保险策略的选择
都具有决定权：保险公司可依据自身风险与收入状况选择分保与否以及分保数
量；同时，再保险公司也可根据风险状况选择承保与否，以及承保的数量。由
此可见，关于再保险策略选择，在合约双方之间存在着一个博弈。一个完备的
再保险合约应兼顾双方的利益，对双方来说都是有利的，再保险合约才能成交。
因此，研究不同博弈情形下最优再保险合约对再保险市场的发展具有重要的理
论价值，且对保险公司购买再保险也有一定的指导意义。
首先，本文以破产概率减小作为再保险双方选择比例再保险合约的依据，
研究最优再保险策略选择问题。假设再保险合约双方均满足扩散风险模型，利
用鞅方法和最优化理论得到了不同博弈情形下的最优比例再保险策略和再保费
满足的条件。通过数值模拟得到了最优分保比例、最优再保费和破产概率与模
型主要参数之间的关系，并结合实际再保险业务给出了相应的解释。研究结论
显示：当保险公司主导时，保险公司的最优自留比例随着再保费的增加而增加，
同时再保险公司选择承保的再保费下界随着保险公司波动率的增加而增加；当
双方共同主导时，最优再保费是分保公司自身保费收入和风险波动率的增函数、
承保公司风险波动率的减函数；当再保险公司占主导时，再保险合约双方的破
产概率均随着分保公司风险的增加而增加。
其次，假设保险公司和再保险公司都以期望终端盈余效用的增加作为再保
险合约成交的条件。在扩散风险模型下，假设保险公司和再保险公司均可以投
资金融市场，考虑了保险公司和再保险公司之间的比例再保险策略选择博弈问
题。在保险公司和再保险公司都具有指数效用函数下，通过构造并求解相应的
HJB方程，得到了不同博弈情形下最优投资-再保险策略的显示表达式，以及再
保费满足的条件。研究结果发现：投资行为均增加了双方的终端盈余效用，且
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扩散风险模型下再保险策略选择博弈研究
风险资产收益率越高，效用收益越明显；当保险公司主导时，保险公司最优自
留比例与再保费存在正向关系，与自身风险厌恶程度与波动率存在负向关系，
且再保险公司选择承保的再保费下界与自身风险厌恶程度也存在正向关系；当
保险公司和再保险公司共同主导时，选择最优再保险策略后，再保险合约双方
均具有效用收益，且当双方风险的相关系数为负时，保险公司获得了更高的终
端效用；当再保险公司主导时，保险公司的效用收益随着再保费增加先升后降，
而再保险公司的效用收益随着再保费的增加而升高。
关键词:比例再保险；再保险保费；破产概率；效用最大化；扩散风险模型
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扩散风险模型下再保险策略选择博弈研究
Abstract
As an important means to maintain the normal operation of an insurance
company, reinsurance refers to the behavior that the insurer insures part of the risks
and responsibilities it underwrites to other insurers by signing reinsurance contracts
on the basis of the original insurance contract. As two different subjects, both parties
to the reinsurance contract have the right to decide on the choice of reinsurance
strategy: insurance companies can choose whether or not to reinsurance and the
number of reinsurance according to their own risk and income status; At the same
time, reinsurance companies can also choose whether to underwrite or not according
to the risk situation, and the number of underwritten. It can be seen that there is a
game between the two sides of the contract about the choice of reinsurance strategy. A
complete reinsurance contract should take into account the interests of both parties,
which is beneficial to both parties, so that the reinsurance contract can be concluded.
Therefore, it is of great theoretical value to study the optimal reinsurance contract
under different game situations for the development of reinsurance market, and it also
has certain guiding significance for insurance companies to buy reinsurance.
Firstly, this paper studies the optimal reinsurance strategy selection based on the
reduction of bankruptcy probability as the basis for both reinsurance parties to choose
proportional reinsurance contracts. Assuming that both sides of the reinsurance
contract meet the diffusion risk model, the optimal proportional reinsurance strategy
and the conditions of reinsurance premium satisfaction under different game
situations are obtained by martingale method and optimization theory. Through
numerical simulation, the relationships between the optimal reinsurance ratio, optimal
reinsurance premium and ruin probability and the main parameters of the model are
obtained, and the corresponding explanations are given in combination with the actual
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