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On moments of the integrated exponential Brownian motion

  • Francesco CaravelliEmail author
  • Toufik Mansour
  • Lorenzo Sindoni
  • Simone Severini
Open Access
Regular Article

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.

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Copyright information

© The Author(s) 2016

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Francesco Caravelli
    • 1
    • 2
    • 3
    Email author
  • Toufik Mansour
    • 4
  • Lorenzo Sindoni
    • 1
  • Simone Severini
    • 3
  1. 1.Invenia LabsCambridgeUK
  2. 2.London Institute for Mathematical SciencesLondonUK
  3. 3.University College LondonLondonUK
  4. 4.University of HaifaHaifaIsrael

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