Numerical computation of the distribution of the sum of correlated log-normal variables

Presenter: Zdravko Botev, UNSW

The distribution of the sum of dependent log-normal variables has numerous applications in, for example, the assessment of insurance risk, the valuation of an asset portfolio driven by the Black-Scholes model, and the performance analysis of wireless communication systems. In this talk we propose the first (quasi) Monte Carlo estimator for the efficient computation of the distribution of the sum of dependent log-normals. We show that the estimator is asymptotically efficient, or robust, in both tails of the distribution. The estimator enjoys the additional advantage that it is infinitely smooth, which yields, not only additional error reduction via Quasi Monte Carlo, but also a simple estimator of the corresponding probability density function - an object of significant interest in communication systems.