https://doi.org/10.1140/epjp/i2016-16245-9
Regular Article
On moments of the integrated exponential Brownian motion
1
Invenia Labs, 27 Parkside Place, CB1 1HQ, Cambridge, UK
2
London Institute for Mathematical Sciences, 35a South Street, W1K 2XF, London, UK
3
University College London, Gower Street, WC1E 6BT, London, UK
4
University of Haifa, 31905, Haifa, Israel
* e-mail: francesco.caravelli@gmail.com
Received:
28
May
2016
Accepted:
23
June
2016
Published online:
27
July
2016
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.
© The Author(s), 2016