(Weighted) Sum of 'n' Correlated Lognormals : Probability Density Function – Numerical calculation

Probability density function (pdf) for (weighted) sum of n correlated lognormal variables is deducted. The method uses joint pdf of multivariate correlated lognormal variables and an extended method of convolution. The formula contains (n-1)-fold integral, which can be evaluated by numerical integration or an alternative direct discrete computing method. As an example a 4 dimensional weighted case is provided, the deducted theoretical pdf is checked by Monte Carlo simulation