On the Laplace transform of the lognormal distribution: Analytic continuation and series approximations

We study the analytical properties of the Laplace transform of the lognormal distribution. Two integral expressions for the analytic continuation of the Laplace transform of the lognormal distribution are provided, one of which takes the form of a Mellin-Barnes integral. As a corollary, we obtain an integral expression for the characteristic function. We present two approximations for the Laplace transform of the lognormal distribution, both valid in C \ (-infinity, 0]. In the last section, we discuss how one may use our results to compute the density of a sum of independent lognormal random variables. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This study explores the analytical properties of the Laplace transform of the lognormal distribution, providing two integral expressions and two approximations. The results are then discussed in terms of computing the density of a sum of independent lognormal random variables.