基于不完全信息和相依结构的最优再保险策略研究

Optimal reinsurance theory is a frontier and hot topic within the international actuarial science community nowadays. The main purpose of this project is to design the form of the optimal reinsurance strategy under the assumptions of incomplete information and dependence structure. First, we adopt the criteria of ruin probability and tail risk measure from the point of the insurer with incomplete information. The optimal reinsurance strategies are derived through De Vylder approximation method and stochastic order theory, respectively. We also compare the obtained results to the optimal reinsurance strategies which are derived under complete information assumption. Second, in dependence structure framework, assume that the underwriting risks are not independent, we study the influence of dependence structure on optimal reinsurance strategy under the multivariate tail risk measure. Third, we evaluate the risk of reinsurance actuarial model through Copula theory. The dependence structure of multivariate risks from the insurance company is characterized by Copula function, where the impact of dependence coefficient on optimal retention for different types of reinsurance contract is analyzed. Finally, as a summary, we are going to explore tentatively some ideas and methods as to combining incomplete information and dependence structure. These exploratory studies will further expand the scope of the research of optimal reinsurance theory.

最优再保险理论是当前国际精算学界研究的前沿与热点。本项目在不完全信息和多重风险相依情形下，考虑最优再保险分出设计问题。首先，基于不完全信息假设，分别以破产概率和尾部风险度量为优化准则，运用De Vylder近似方法和随机序理论对优化模型进行分析，探究保险公司的最优再保险策略，并与完全信息下保险公司最优再保险策略进行比较。其次，在相依结构框架下，考虑个体风险之间的相关性，通过构建以多元尾部风险度量为优化准则的再保险模型，研究相依结构对保险公司最优再保险策略的影响。再次，运用Copula理论对再保险精算模型进行风险评估，通过使用不同的Copula函数来描述保险公司各种风险之间的相依关系，并量化分析相依系数对不同再保险合约最优自留额的影响。最后，在此基础上，初步探讨综合不完全信息和多重风险相依假设的最优再保险策略的一些思路和方法。这些探索将进一步拓展最优再保险理论研究。

最优再保险理论是当前国际精算学界研究的前沿与热点。本项目主要基于个体不完全信息假设，在风险模型中引入再保险合约，运用De Vylder 近似方法对模型进行重新设定并依据有限的信息对再保险保费进行估计，通过最小化保险公司的破产概率得出再保险合约的最优自留额。其次，考虑索赔次数之间的序列相关性，研究保单组合尾部风险度量的计算问题，从个体风险之间的相依结构出发，系统展开基于copula 理论的相依风险模型的最优再保险策略的研究工作。再次，利用极值copula 描述承保业务损失之间的相依关系并以此构建再保险精算风险模型。考虑在不同门限值下如何确定两类极端事件的重现期以及在不同免赔额和责任限额下如何厘定超额赔付再保险的保费和线率。以上研究借助精算学中的经典相依风险模型、多元统计建模与仿真技术、风险管理中的多元风险测度理论，探讨不同相依结构下保险公司的最优再保险策略并分析不同形式的再保险策略对保险公司财务状况的动态影响。这些探索进一步拓展了风险模型最优再保险理论研究。