中文摘要：

本文考虑当理赔次数N分布为Poisson-逆高斯分布时，相应的总理陪量分布（即复合Poisson-逆高斯分布）的两种近似：正态分布和平移Gamma分布。同时还考虑了当理赔量的分布为下指数分布时复合Poisson-逆高斯分布的尾概率的一种近似计算。

英文摘要：

With the Poisson-inverse Gaussian distribution choice for the distribution of the number of claims, a compound Poisson-inverse Gaussian distribution as the distribution of aggregate claims is considered. The normal distribution and the translated gamma distribution are employed as two kinds of approximations to the compound Poisson-inverse Gaussian distribution under some requirements. Also the approximation to the tail probability of compound Poisson-inverse Gaussian distribution is given when the claim amount distribution is subexponential.