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Revisiting integral functionals of geometric Brownian motion

Author

Listed:
  • Elena Boguslavskaya
  • Lioudmila Vostrikova

    (LAREMA - Laboratoire Angevin de Recherche en Mathématiques - UA - Université d'Angers - CNRS - Centre National de la Recherche Scientifique)

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 µ ∈ R, σ > 0, and $(W_s )_s>0 $i s 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," Working Papers hal-02461094, HAL.
    • Handle: RePEc:hal:wpaper:hal-02461094
    Note: View the original document on HAL open archive server: https://hal.science/hal-02461094
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