离散时间相依复合二项风险模型中一些风险精算量的概率递推公式  

The Probability Recursive Formulas of Some Actuarial Values in a Discrete Time Interaction Compound Binomial Risk Model

作　　者：罗辑 韩树新[2] Luo Ji;Han Shuxin(School of Mathematical Sciences,Nankai University,Tianjin 300071,China;School of Mathematics and Statisticy Hebei University of Economics and Business,Shijiazhuang 050061,China)

机构地区：[1]南开大学数学科学学院,天津300071 [2]河北经贸大学数学与统计学院,河北石家庄050061

出　　处：《南开大学学报（自然科学版）》2022年第1期15-21,共7页Acta Scientiarum Naturalium Universitatis Nankaiensis

摘　　要：推导出具有随机收益过程和时间相依索赔的时间离散复合二项风险模型中与某些精算值相关的概率的递推公式.在这个模型中,假设有两类不同分布的索赔,并允许间接索赔延迟.模型中的随机收益过程也是一个复合二项过程.考虑了在固定的时间段内与4个精算量相关的概率值.4个精算量分别是:发生的主要索赔的数量、无索赔的最长连续时间段的长度、无索赔的最短连续时间段的长度以及无索赔的连续时间段的数量.The recursive formulas of the probabilities relate to some actuarial values in a time discrete interaction compound binomial risk model with a stochastic income process and time-correlated claims are derived.In this model,there are two classes of distribution of claims and allow the by-claims to delay.The stochastic income process is also a compound binomial process.In a fixed time horizon,the probabilities that relate to the number of main claims occurred,the length of the longest continuous time periods of no claim,the length of the shortest continuous time periods of no claim,and the number of the continuous time periods of no claim are considered.

关 键 词：复合二项风险模型 时间相依 随机收入 风险精算量 

分 类 号：O211.6[理学—概率论与数理统计]