基于保单进入过程的风险系统的建构与应用研究

保险风险理论是风险管理的主要内容，但是经典的风险模型无法对现代保险实务进行深入细致的描述。本项目根据保险实际运营过程，依据保单的进入过程，通过发射噪声过程理论的指导，构建一类基于保单进入过程的新的保险风险模型。结合重尾分布理论、多元相依风险理论以及随机过程理论的研究前沿，探索这一新的风险系统的概率性质及统计推断结果，为保险实际工作提供有益的建议和理论指导。首先构造多种噪声过程，建立基于保单进入过程的保险风险模型体系，研究当索赔量是各种重尾相依随机变量时风险过程的极限性质、破产概率的渐近表达式、精细大偏差等精算量的性质；其次尝试在此基础上探索一般发射噪声过程的理论结果；最后将理论研究结果与模拟分析方法相结合，收集处理保险实际数据，提出符合甘肃实际情况的风险预测和管理模型。本项目的完成，不仅具有丰富保险风险理论和方法的重要价值，而且将对甘肃省保险业的风险管理提供理论依据和技术支撑。

Insurance Risk Theory is one of the key components of risk management theory. However, it has been identified that the classical risk model is unable to provide an in-depth description of the insurance business practices today. Guided by the Theory of Shot Noise Process, this project aims to build a new risk management model for insurance business in line with the actual operating flow based on the entry process of insurance policy. Combined with heavy-tailed distribution theory, the multi-dependency theory and the research frontier of stochastic process theory, this project explores the statistical nature of the risk management system and the results from statistical inferences in order to provide some useful recommendations and theoretical guidance to insurance business in practice. First, we construct various noise processes and build the system of insurance risk model based on the policy entry process. At the same time, we study the limit properties of the risk process, asymptotic formulas of ruin probability, large derivations and other actuarial quantities under the assumptions that the claim amount belongs to the family of heavy-tailed dependent random variables. Second, on the basis of the first stage, we explore the theoretical results of the Shot Noise Process, and finally we combine the theoretical research results and the methodology of simulation analysis, and analyze business data collected from real business to propose a risk forecast and management model for insurance business in Gansu Province. The completion of this project not only enriches risk management theory and methodology of insurance business, but provides theoretical basis and technical guidance to risk management in insurance business in Gansu Province.