Abstract: The bivariate Poisson models of contingent claim times about the homogeneous portfolios are studied, and an independent condition of the two variables is proved, and then the Mixed bivariate Poisson models of contingent claim times about the heterogeneous portfolios with dependent risks are studied, and the last, the optimum BMS formula about the heterogeneous portfolios with dependent risks are reached.

Key words: risk dependence, bivariate Poisson, mixed Poisson, BMS

摘要： 研究了同质风险相依条件下的二元Poisson索赔次数模型，得到了二元Poisson索赔次数模型独立的充分必要条件；同时研究了非同质风险相依条件下二元混合Poisson索赔次数模型，得到了相应的非同质风险保单组合的索赔次数模型为双变量负二项分布的概率函数；在此基础上将保险精算中的最优BMS由独立情形推广到了风险相依的情形，并得到了相应的最优BMS的计算公式。

关键词: 风险相依, 双变量Poisson分布, 混合Poisson分布, 最优BMS