Two numerical methods are proposed to numerically evaluate the survival function of a compound distribution and the stop-loss premiums associated with a non-proportional global reinsurance treaty. The first method relies on a representation of the probability density function in terms of Laguerre polynomials and the gamma density, the second is a numerical inversion of the Laplace transform. Numerical comparisons are conducted at the end of the paper. MSC 2010: 60G55, 60G40, 12E10.