同单调相依结构下两重生命模型的概率分布

在寿险实务中,在处理涉及到多个生命的问题时往往假设各个生命之间是独立的,但事实上,因为受某些相同因素影响的生命之间总是存在一定的正相依性．本文证明了在给定边际分布的二维随机向量中,同单调相依结构是在相关序意义下最强的正相依结构,研究了在此相依结构下的两重生命模型的概率分布,并给出了随机序意义下两个状态消亡时间的随机上界和随机下界．

The Probability Distribution of The Two-life Model Based on Comonotonic Dependence Structure

In life insurance practice, when more than one life are involved they are often assumed to be independent. But it is deemed to be positively dependent among lives that are affected by some same factors. In this paper, in the sense of correlation order, we prove that the comonotonic random vector has the strongest positively dependent structure among binomial random vectors which have the same marginals. Also we study the probability distribution of the two-life model based on the corresponding dependent structure, and obtain the stochastic upper and lower bounds of the remaining life of two status in the sense of stochastic order.