保险风险和金融风险交互作用下极端风险的建模及定量分析

China has been vigorously promoting the construction of the catastrophe insurance system, but the current progress is still slow. One important reason is that the catastrophe risk management system of insurance companies in our country is still not perfect, especially after the introduction of reinsurance, bonds, securities and other means of risk transfer, how to avoid that the systemic risk by extreme events brings the fatal impact to the financial and insurance industry under the actual situation of the large population and frequent natural disasters in China. Therefore, the theory study of the catastrophe systemic risk in accordance with the national conditions of China has become a key factor to promote the construction of the catastrophe insurance system in China. . This project takes into account the correlation of multiple risk factors in a stochastic economic environment with the interplay of insurance and financial risks, describes extreme risks with heavy tailed random variables, uses the tail-related risk measure as the quantitative index of risks of extreme events, analyzes the interplay influence of the two kinds of risk on the solvency of insurance companies quantificationally, and resolves the measure problems of the risk that insurance companies are facing disaster products or the estimation problems of the (financial) systemic risks triggered by extreme events. Based on the results obtained, we do the simulation analysis of rare events, develop a systematic method of the modeling and measurement of extreme risks in the insurance market under the interplay of insurance and financial risks, and provide the theoretical basis on the practice of extreme risk measurement for insurance industries.

我国已在大力推进巨灾保险制度建设，但目前的进展依然缓慢。一个重要的原因是我国保险公司的巨灾风险管理体系仍然未完善，尤其是引入了再保险、债券、证券化等风险转移手段后，如何能够在我国人口多、自然灾害频发的实际情况下，避免系统风险的发生带给金融保险行业致命冲击。由此，进行符合我国国情的巨灾系统风险理论研究，成为推动我国巨灾保险制度建设的关键一环。. 本项目考虑保险风险与金融风险交互作用的随机经济环境中多种风险因素的相关性，用重尾随机变量刻画极值风险，采用与尾相关的风险度量作为保险公司面临极端事件的风险度量，定量地分析两种风险的交互作用对保险公司偿付能力的影响，解决保险公司面临灾难产品的风险度量或极端事件引发(金融)系统风险的估计问题。在所得结果的基础上，做稀有事件仿真分析，发展一套保险和金融风险交互作用下保险市场中极端风险建模与度量的系统化方法，为保险业极端风险度量实践提供理论依据。

金融保险风险管理方面关于保险风险和金融风险交互作用下风险模型风险度量的估计和计算问题，越来越受到关注。考虑随机经济环境中多风险交错相关，采用与尾相关的风险度量，定量分析两种风险的交互作用对保险公司面临极端事件偿付能力的影响，解决保险公司面临灾难产品的风险度量或极端事件引发(金融)系统风险的估计问题。在所得结果的基础上进行数值模拟分析，发展一套保险和金融风险交互作用下保险市场中极端风险建模与度量的系统化方法，为保险业极端风险度量实践提供理论依据。同时，设计了帕累托最优再保险合同，进行分层再保险。最后，将概率极限理论及其方法，应用到高维的随机场极值的尾渐近，随机变量加权和的完全矩收敛，强大数定律，及网络系统的可靠性。主要结论是：.1) 重要研究进展在于考虑多相依结构，保险风险和金融风险服从的相依结构适用范围较广。引入了一般的自适应càdlàg过程刻画随机投资回报过程，归咎于大量证据表明一些金融资产通常表现出非独立和非平稳的增量，其收益和这些收益的波动性如下通常呈负相关等。通过多维更新风险模型刻画相依的不同业务线的索赔规模，应用到如Lévy过程、Vasicek利率模型，Cox-Ingersoll-Ross利率模型、Heston模型和随机波动率模型等重要的随机过程，通过蒙特卡罗模拟验模型的有效性。.2) 再保险方面，设计了帕累托最优再保险合同通过最小化保险人负债的风险调整值和再保险人的负债。当再保险保费原则满足三个公理，发现层再保险总是最佳的风险度量，进行分层再保险。.3) 研究高维的高斯随机场极值的尾渐近，多维极值的联合尾渐近性，及相关的多维再生模型。为保险公司提供更多关于相依风险模型中巨灾保险风险度量方法的理论依据。.4) 发展概率论中极限的一些理论，比如随机变量加权和的完全矩收敛，或具有ANA序列产生的随机系数的线性过程的强大数定律，推动概率极限理论的发展。.5) 将概率理论应用到网络物理系统可靠性中，提出了最优防御在攻击优化策略下的部署策略，为建立了一个系统以预警机制为核心的可传播网络防御模型提供了理论依据。