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An approximate formula for the first-crossing-time density of a Wiener process perturbed by random jumps

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  • Giraudo, Maria Teresa

Abstract

An approximate solution to an integral equation for the first-crossing-time density of a Wiener process with constant amplitude jumps separated by exponential random times is shown to hold under suitable conditions and to explain some multimodal behaviors.

Suggested Citation

  • Giraudo, Maria Teresa, 2009. "An approximate formula for the first-crossing-time density of a Wiener process perturbed by random jumps," Statistics & Probability Letters, Elsevier, vol. 79(13), pages 1559-1567, July.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:13:p:1559-1567
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    References listed on IDEAS

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    1. Victor Vaugirard, 2004. "A canonical first passage time model to pricing nature-linked bonds," Economics Bulletin, AccessEcon, vol. 7(2), pages 1-7.
    2. Maria Teresa Giraudo & Laura Sacerdote & Cristina Zucca, 2001. "A Monte Carlo Method for the Simulation of First Passage Times of Diffusion Processes," Methodology and Computing in Applied Probability, Springer, vol. 3(2), pages 215-231, June.
    3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    4. repec:ebl:ecbull:v:7:y:2004:i:2:p:1-7 is not listed on IDEAS
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