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Some conditional crossing results of Brownian motion over a piecewise-linear boundary

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  • Abundo, Mario

Abstract

Explicit formulae are found for the probability that the Brownian motion, Bt, up-crosses, in [0,T], a piecewise-linear function S(t), with the condition that the value of Bt is assigned at a future time u>T or at an intermediate time u

Suggested Citation

  • Abundo, Mario, 2002. "Some conditional crossing results of Brownian motion over a piecewise-linear boundary," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 131-145, June.
    • Handle: RePEc:eee:stapro:v:58:y:2002:i:2:p:131-145
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    Citations

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    Cited by:

    1. Abundo, Mario, 2012. "An inverse first-passage problem for one-dimensional diffusions with random starting point," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 7-14.
    2. Klepper, Steven & Thompson, Peter, 2010. "Disagreements and intra-industry spinoffs," International Journal of Industrial Organization, Elsevier, vol. 28(5), pages 526-538, September.
    3. Bischoff, Wolfgang & Hashorva, Enkelejd, 2005. "A lower bound for boundary crossing probabilities of Brownian bridge/motion with trend," Statistics & Probability Letters, Elsevier, vol. 74(3), pages 265-271, October.
    4. Stoyan Valchev & Radu Tunaru & Frank J. Fabozzi, 2015. "Multiperiod conditional valuation of barrier options with incomplete information," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1093-1102, July.
    5. Mario Abundo, 2010. "On the First Hitting Time of a One-dimensional Diffusion and a Compound Poisson Process," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 473-490, September.
    6. Atkinson, Michael P. & Singham, Dashi I., 2015. "Multidimensional hitting time results for Brownian bridges with moving hyperplanar boundaries," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 85-92.
    7. Stefan Ankirchner & Christophette Blanchet-Scalliet & Nabil Kazi-Tani & Chao Zhou, 2019. "Gambling for resurrection and the heat equation on a triangle," Working Papers hal-02405853, HAL.
    8. Abundo, Mario, 2013. "The double-barrier inverse first-passage problem for Wiener process with random starting point," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 168-176.
    9. Lee, Taeho, 2023. "Exact simulation for the first hitting time of Brownian motion and Brownian bridge," Statistics & Probability Letters, Elsevier, vol. 193(C).
    10. Qinglai Dong & Lirong Cui, 2019. "First Hitting Time Distributions for Brownian Motion and Regions with Piecewise Linear Boundaries," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 1-23, March.
    11. Stefan Ankirchner & Christophette Blanchet-Scalliet & Nabil Kazi-Tani & Chao Zhou, 2021. "Gambling for resurrection and the heat equation on a triangle," Post-Print hal-02405853, HAL.

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