连续时间复合二项模型多维精算量的联合分布

连续时间复合二项模型是由文献首先提出的.作为离散时间复合二项模型的连续化版本,连续时间复合二项模型的极限形式即为经典风险模型.为了得到该模型多维精算量的联合分布,该文引入了一列上穿零点,推导出该列上穿零点所构成的缺陷(defective)更新序列的更新质量函数.利用此更新质量函数及余额过程的强马氏性可以得到破产概率和包含破产时间,破产前余额,破产严重程度,破产前最大盈余,破产到恢复的最大赤字,整个过程的最大赤字等多维精算量的联合分布.由此联合分布得到其1-骨架链—离散时间复合二项模型的对应的联合分布,最后给出在1-骨架链中索赔额服从指数分布时这一特殊情况下相应多维精算量的联合分布的明确表达式.

Joint Distributions of Some Actuarial Random Vectors in the Continuous-time Compound Binomial Model

The continuous-time compound binomial model, firstly proposed by1], is the continuous-time version of the compound binomial model. In this paper, a renewal mass function of a defective renewal sequence constituted by the up-crossing zero points is introduced in the continuous-time compound binomial model. By the mass function together with the strong Markov property of the surplus process X(t), the explicit expressions of the ruin probability and the joint distributions of some actuarial random vectors such as (T, X(T-), |X(T)|), (T, X(T-), |X(T)|, inf_{0≤tX(t)) and (T, X(T-), |X(T)|, sup0≤tX(t)) are obtained, where T represents the time of ruin and L the time of the surplus process leaving deficit ultimately. The corresponding joint distributions are directly obtained for the compound binomial model, {X(n)}, as the 1-skeleton chain of the continuous-time compound binomial model. Finally, a special case with the claim amount being geometrically distributed in the compound binomial model is considered.}