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Revisiting integral functionals of geometric Brownian motion

Author

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  • Elena Boguslavskaya

    (LAREMA)

  • Lioudmila Vostrikova

    (LAREMA)

Abstract

In this paper we revisit the integral functional of geometric Brownian motion $I_t= \int_0^t e^{-(\mu s +\sigma W_s)}ds$, where $\mu\in\mathbb{R}$, $\sigma > 0$, and $(W_s )_s>0$ is a standard Brownian motion. Specifically, we calculate the Laplace transform in $t$ of the cumulative distribution function and of the probability density function of this functional.

Suggested Citation

  • Elena Boguslavskaya & Lioudmila Vostrikova, 2020. "Revisiting integral functionals of geometric Brownian motion," Papers 2001.11861, arXiv.org.
    • Handle: RePEc:arx:papers:2001.11861
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    References listed on IDEAS

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    1. Daniel Dufresne, 2000. "Laguerre Series for Asian and Other Options," Mathematical Finance, Wiley Blackwell, vol. 10(4), pages 407-428, October.
    2. De Schepper, A. & Goovaerts, M. & Delbaen, F., 1992. "The Laplace transform of annuities certain with exponential time distribution," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 291-294, December.
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