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Integral Representations for the Hartman–Watson Density

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  • Yuu Hariya

    (Tohoku University)

Abstract

This paper concerns the density of the Hartman–Watson law. Yor (Z Wahrsch Verw Gebiete 53:71–95, 1980) obtained an integral formula that gives a closed-form expression of the Hartman–Watson density. In this paper, based on Yor’s formula, we provide alternative integral representations for the density. As an immediate application, we recover in part a result of Dufresne (Adv Appl Probab 33:223–241, 2001) that exhibits remarkably simple representations for the laws of exponential additive functionals of Brownian motion.

Suggested Citation

  • Yuu Hariya, 2022. "Integral Representations for the Hartman–Watson Density," Journal of Theoretical Probability, Springer, vol. 35(1), pages 209-230, March.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:1:d:10.1007_s10959-020-01067-0
    DOI: 10.1007/s10959-020-01067-0
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    References listed on IDEAS

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    1. M. Schroder & P. Carr, 2003. "Bessel processes, the integral of geometric Brownian motion, and Asian options," Papers math/0311280, arXiv.org.
    2. Hariya, Yuu, 2020. "On some identities in law involving exponential functionals of Brownian motion and Cauchy random variable," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 5999-6037.
    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.
    Full references (including those not matched with items on IDEAS)

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