Limit of the sum of two groups of lognormal sums

Abstract

This paper derives limit distributions for the sum of two groups of correlated lognormal variables. The within group correlations are equal and the overall covariance matrix has a specific block structure. We prove that the normalized sum of the two groups of lognormal variables converges to a weighted sum of two correlated lognormal variables.

Keywords: Lognormal sums, limits, block correlation matrix

JEL Classification: C10