Fast and Accurate Computation of the Distribution of Sums of Dependent Log-Normals

We present a new Monte Carlo methodology for the accurate estimation of the distribution of the sum of dependent log-normal random variables. The methodology delivers statistically unbiased estimators for three distributional quantities of significant interest: the left tail, or cumulative distribution function; the probability density function; and the right tail, or complementary distribution function of the sum of dependent log-normals. In all of these three cases our methodology delivers fast and highly accurate estimators in settings for which existing methodology delivers biased estimators with large variance. We provide insight into all the computational challenges using both theoretical results and numerical experiments.