In this paper, we are interested in the dependence between lifetimes based on a joint survival model. This model is built using the bivariate Sarmanov distribution with Phase-Type marginal distributions. Capitalizing on these two classes of distributions’ mathematical properties, we drive some useful closed-form expressions of distributions and quantities of interest in the context of multiple-life insurance contracts. The dependence structure that we consider in this paper is based on a general form of kernel function for the Bivariate Sarmanov distribution. The introduction of this new kernel function allows us to improve the attainable correlation range.

在本文中，我们对基于联合生存模型的生命周期之间的依赖性感兴趣。该模型是使用具有相位型边缘分布的二元 Sarmanov 分布构建的。利用这两类分布的数学特性，我们在多人寿保险合同的背景下驱动了一些有用的分布和感兴趣数量的封闭形式表达式。我们在本文中考虑的依赖结构基于双变量 Sarmanov 分布的核函数的一般形式。这个新核函数的引入使我们能够提高可达到的相关范围。