基于贝叶斯分位数回归的地震巨灾风险分摊体系研究

地震灾害通常会导致巨额损失，需要由投保人、保险公司、再保险公司、政府以及资本市场等多主体共同合作，形成多层次风险分摊体系才能应对地震巨灾风险。该风险分摊体系的建立主要依赖于对地震巨灾风险的准确评估，并在此基础上确定合理的分摊方案。因此，本项目提炼出风险分摊体系中的关键科学问题，包括风险评估、费率厘定以及最优风险分摊方案，从理论上研究解决这些问题的统计模型与方法。具体研究内容包括：第一、根据地震巨灾风险的特征，提出带有空间效应的分位数回归模型，并探讨其贝叶斯统计推断方法；第二、在分位数回归的基础上评估地震巨灾风险，并研究巨灾保险定价原理；第三、在风险评估和定价基础上，基于分位数构建效用函数，确定最优分摊方案。最后，收集地震灾害数据，应用所提出的理论和方法对地震灾害进行分析，构建出完善的地震巨灾风险多层次分摊体系，为我国地震巨灾风险管理提供决策建议。

Earthquakes often result in catastrophic losses, and multil-level risk allocation system constructed with multiple participators like insureed, insurer, reinsurer, government and financial market is needed to deal with earthquake catastophe risk. The most important issues in constructing of this system include the evaluation of earthquake risk and a reasonable risk allocation scheme. Therefore, this project will discuss the key issues in multil-level risk allocation system, including risk analysis, rate making and optimal coverage limits for different participators. New statistical models and methodologies will be developed to solve these problems. The specific research contents include as following: Firstly, a quantile regression with spatial effect is proposed according to the characteristics of earthquake risk, and its Baysian statistical inferences will be discussed. Secondly, earthquake catastrophic risk will be analyzed based on the proposed model and methods, and catastrophic insurance pricing principle will then be discussed. Thirdly, an utility function based on quantiles will be develped and the optimal risk allocation scheme will be obtained. Finally, the proposed models and methods will be used to analyze the loss data caused by earthquake, and a completely multi-level risk allocation system for earthquake catastrophic risk will be established. According to the research results, suggestions for earthquake risk management will be proposed.