摘要：The distribution function of the sum of random variables plays an important role in the management of portfolios and consequently in actuarial science. However it is generallyproblematic and so some approximations have been introduced. Though all approximation s show error, one of the best distribution functions for approximation is the Compound Poisson distribution function. In order to improve the distribution approximation of the sum of the random variables, finding the upper bound is of crucial importance. My focus is mostly on upper bounds of approximation that have no restriction on distribution of random variables, and the results are in a better order than bounds previously reported. We review these bounds and compare them. In the end, we applied them to a real portfolio.
