稀疏过程在常利率环境下的广义Poisson风险模型中的应用
Application of Sparse Process in Generalized Poisson Risk Model under Constant Interest Rate Environment

风险理论是连接数学与金融问题的一座桥梁，它是保险精算学(即实际寿险精算)的重要组成部分，是保险精算人员对保险业务进行风险管理的重要理论工具，同时也是保险公司发展业务进行有效营运的理论保证。破产概率是风险理论研究的核心问题，而利息是影响破产概率的重要因素。本文讨论了常利率环境下离散时间风险模型的破产概率，给出了模型的破产概率的上界。首先构造了风险模型，通过鞅方法得到模型的破产概率满足的Lundberg不等式和相关公式；然后给出了离散时间情形下的双险种风险模型，得到了与破产相关的一些变量的表达式和性质。
Risk theory is a bridge connecting mathematics and financial problems, it is an important component of insurance actuarial science, it is an important theoretical tool for insurance actuaries to manage risks in insurance business, and also a theoretical guarantee for insurance companies to develop and operate effectively .Bankruptcy probability is a core issue in risk theory research, and interest is an important factor affecting bankruptcy probability. In this paper, the ruin probability of discrete time risk model under constant interest rate is discussed, and the upper bound of bankruptcy probability is given. Firstly, the risk model is established, and the Lundberg inequality and general formula of ruin probability are given by using martingale method. Secondly, the risk model of double insurance in the situation of discrete time is established, and the distribution of surplus before bankruptcy and the recursion formula of the distribution of bankruptcy duration are obtained.