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On positive and negative moments of the integral of geometric Brownian motions

Author

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  • Donati-Martin, Catherine
  • Matsumoto, Hiroyuki
  • Yor, Marc

Abstract

We present explicit formulae for the positive and negative moments of an exponential Wiener functional, which is defined as the integral with respect to time of geometric Brownian motion and plays an important role in several fields.

Suggested Citation

  • Donati-Martin, Catherine & Matsumoto, Hiroyuki & Yor, Marc, 2000. "On positive and negative moments of the integral of geometric Brownian motions," Statistics & Probability Letters, Elsevier, vol. 49(1), pages 45-52, August.
    • Handle: RePEc:eee:stapro:v:49:y:2000:i:1:p:45-52
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    Cited by:

    1. De Schepper, Ann & Goovaerts, Marc & Dhaene, Jan & Kaas, Rob & Vyncke, David, 2002. "Bounds for present value functions with stochastic interest rates and stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 87-103, August.
    2. Ghomrasni, Raouf & Graversen, Svend Erik, 2002. "An extension of Seshadri's identities for Brownian motion," Statistics & Probability Letters, Elsevier, vol. 59(4), pages 379-384, October.
    3. Andrew Lyasoff, 2016. "Another look at the integral of exponential Brownian motion and the pricing of Asian options," Finance and Stochastics, Springer, vol. 20(4), pages 1061-1096, October.
    4. Hariya, Yuu, 2024. "Invariance of Brownian motion associated with exponential functionals," Stochastic Processes and their Applications, Elsevier, vol. 167(C).

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