On the moments of the integrated geometric Brownian motion

This note demonstrates how the divided differences characterization for the moments of the integrated geometric Brownian process arises naturally from the solution to their differential equations. The characterization was introduced by Baxter and Brummelhuis in their paper (Baxter and Brummelhuis (2011)) where they demonstrate its consistency with the results found by Oshanin et al. (1993). Here we demonstrate its validity with more general expressions presented in other papers and explore the divided differences characterization of these moments further.