Comonotonic and moment matching approximations for sums of lognormal random variables

Abstract

In this paper, based on the concept of weighted distribution, we introduce a kind of new approximations for sums of lognormal random variables, such that they are both comonotonic and moment matching. Numerical results show that the approximation performance of the newly presented approximations is, overall, comparable to the classical comonotonic approximations, but in terms of the right tail of the distribution of the original sum our approximations perform better than the classical comonotonic ones. Another contribution of this article is the establishment of the step-weighting theory for continuous random variables.