Sampling from characteristic/moment generating function

Suppose I am given a probability distribution only via its characteristic or moment generating function and I want to sample from that distribution to generate paths in a Monte Carlo simulation. Is there a way to sample from the distribution other than numerically inverting the transform and then using conventional methods like the inversion method or acceptance rejection? In my specific case I want to sample paths of the integrated CIR process for which the Laplace transform of the transition probabilities is known. Since the transition probabilities of the CIR processs are knwon explicitely I could approximate the transition probabilities of the integrated CIR process by using the Trapez rule for example. But what do I do if a want an unbiased sample?

• Check this paper by Devoye (1981). – Xi'an Jul 23 '18 at 10:24
• Unfortunately one has to pay for the article linked. However, I found the following paper by the same author: sciencedirect.com/science/article/pii/0898122181900389 Is the approach outlined here the same as in the paper you suggested? Besides, in this algorithm one still needs to evaluate a Fourier integral (only at one point, but still). Is there no method around to sample with only explicit formulas? Is there in any case a simulation algorithm for the integrated CIR process? – lbf_1994 Jul 23 '18 at 13:47
• There was a question in 2011 on the quantitative finance forum, with no answer, which makes the plain resolution doubtful. – Xi'an Jul 23 '18 at 15:09
• @lbf_1994 - could you please point me a reference (maybe also a dataset) about your problem? As I mentioned in my answer below, I was working on an alternative method for the Laplace inversion and I could maybe use your problem as example. – Gi_F. Dec 11 '18 at 11:06