While modeling the dependence structure between several (re)insurance losses by an additive risk factor model, the infinite divisibility is a very desirable property. Unfortunately, if many useful distributions are infinitely divisible, computing the distributions of their pieces is usually a challenging task that requires heavy numerical computations. We propose an estimation algorithm for multivariate generalized gamma convolutions through Laguerre expansions. These distributions are divisible and usefull in dependence structure modeling.