On moments of the integrated exponential Brownian motion

Francesco Caravelli; Toufik Mansour; Lorenzo Sindoni; Simone Severini

doi:10.1140/epjp/i2016-16245-9

On moments of the integrated exponential Brownian motion

Francesco Caravelli, Toufik Mansour, Lorenzo Sindoni, Simone Severini

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	245
Journal	European Physical Journal Plus
Volume	131
Issue number	7
DOIs	https://doi.org/10.1140/epjp/i2016-16245-9
State	Published - 1 Jul 2016

Bibliographical note

Publisher Copyright:
© 2016, The Author(s).

ASJC Scopus subject areas

General Physics and Astronomy
Fluid Flow and Transfer Processes

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10.1140/epjp/i2016-16245-9

Cite this

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abstract = "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 It{\^o}'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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AU - Severini, Simone

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AB - 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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On moments of the integrated exponential Brownian motion

Abstract

Bibliographical note

ASJC Scopus subject areas

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