On moments of the integrated exponential Brownian motion

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作者：
Francesco Caravelli
Toufik Mansour
Lorenzo Sindoni
Simone Severini
机构：
[1] Invenia Labs,
[2] London Institute for Mathematical Sciences,undefined
[3] University College London,undefined
[4] University of Haifa,undefined
来源：
The European Physical Journal Plus | / 131卷
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摘要：
We present new exact expressions for a class of moments of the geometric Brownian motion in terms of determinants, obtained using a recurrence relation and combinatorial arguments for the case of a Itô'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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