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A result on the first-passage time of an Ornstein-Uhlenbeck process

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  • Ditlevsen, Susanne

Abstract

Consider the first time an Ornstein-Uhlenbeck process starting from zero crosses a constant positive threshold. Assuming that the asymptotic mean is above the threshold, conditions on the asymptotic variance relative to the distance between the threshold and the asymptotic mean are given that ensures the finiteness of the positive Laplace transforms.

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  • Ditlevsen, Susanne, 2007. "A result on the first-passage time of an Ornstein-Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1744-1749, December.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:18:p:1744-1749
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    References listed on IDEAS

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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Olivier Scaillet & Boris Leblanc, 1998. "Path dependent options on yields in the affine term structure model," Finance and Stochastics, Springer, vol. 2(4), pages 349-367.
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    Cited by:

    1. Wang, Huiqing & Yin, Chuancun, 2008. "Moments of the first passage time of one-dimensional diffusion with two-sided barriers," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3373-3380, December.
    2. Wergen, Gregor, 2014. "Modeling record-breaking stock prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 396(C), pages 114-133.
    3. Huang, Lu-Jing & Kim, Kyung-Youn & Mao, Yong-Hua & Wang, Tao, 2022. "Variational formulas for the exit time of Hunt processes generated by semi-Dirichlet forms," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 380-399.

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