On moments of the integrated exponential Brownian motion
Francesco Caravelli, Toufik Mansour, Lorenzo Sindoni, Simone Severini
TL;DR
This paper derives new exact formulas for moments of geometric Brownian motion using determinants and applies these to compute averages of solutions to the logistic stochastic differential equation, comparing results with Monte Carlo simulations.
Contribution
It introduces novel exact determinant-based expressions for moments of geometric Brownian motion and demonstrates their application to stochastic differential equations.
Findings
Exact determinant formulas for moments of geometric Brownian motion
Application of formulas to logistic SDE solution averaging
Comparison showing consistency with Monte Carlo results
Abstract
We present new exact expressions for a class of moments for the geometric Brownian motion, in terms of determinants, obtained using a recurrence relation and combinatorial arguments for the case of a Ito's Wiener process. We then apply the obtained exact formulas to computing averages of the solution of the logistic stochastic differential equation via a series expansion, and compare the results to the solution obtained via Monte Carlo.
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