更新风险过程下理赔额的矩研究
On Moments of Claim Amount under the Renewal Risk Process
DOI: 10.12677/sa.2025.1410281, PDF,    科研立项经费支持
作者: 王佳瑀：安徽职业技术大学计算机与信息技术学院，安徽 合肥；王后春：安徽建筑大学数理学院，安徽 合肥
关键词: 更新风险过程；矩；瑕疵更新方程；破产概率；Renewal Risk Process； Moment； Defective Renewal Equation； Ruin Probability
摘要: 提出带有任意理赔间隔时间分布和理赔额分布的更新风险模型。在该模型下给出破产前最后一次理赔额的各阶矩满足的瑕疵更新方程。由此方程通过拉普拉斯变换获得上述各阶矩(包含破产概率)的显示表达式，并在指数理赔条件下给出破产概率的明确表达式。就理赔额服从指数分布，且理赔间隔时间服从Gamma分布和广义Gamma分布的情形，分别给出数值例子，分析相关参数对破产概率的影响，验证了上述结论的有效性。
Abstract: A renewal risk model is proposed where the interclaim time distribution and the claim amount distribution are assumed to be arbitrary, respectively. Under this model, a defective renewal equation is given that is satisfied by the moments of each order of the last claim before ruin which led to ruin. From this equation, the Laplace transform is used to obtain an explicit expression for the above moments including the ruin probability, and another explicit expression for the ruin probability is given under exponential claim condition. In the case that the claim amount obeys the exponential distribution and the interclaim time obeys the Gamma distribution and the generalized Gamma distribution, numerical examples are given to analyze the influence of the relevant parameters on the ruin probability, and the validity of the above conclusions is verified.
文章引用：王佳瑀, 王后春. 更新风险过程下理赔额的矩研究[J]. 统计学与应用, 2025, 14(10): 32-40. https://doi.org/10.12677/sa.2025.1410281

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