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On the First-Passage Area of a One-Dimensional Jump-Diffusion Process

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  • Mario Abundo

    (Università “Tor Vergata”)

Abstract

For a one-dimensional jump-diffusion process X(t), starting from x > 0, it is studied the probability distribution of the area A(x) swept out by X(t) till its first-passage time below zero. In particular, it is shown that the Laplace transform and the moments of A(x) are solutions to certain partial differential-difference equations with outer conditions. The distribution of the maximum displacement of X(t) is also studied. Finally, some explicit examples are reported, regarding diffusions with and without jumps.

Suggested Citation

  • Mario Abundo, 2013. "On the First-Passage Area of a One-Dimensional Jump-Diffusion Process," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 85-103, March.
    • Handle: RePEc:spr:metcap:v:15:y:2013:i:1:d:10.1007_s11009-011-9223-1
    DOI: 10.1007/s11009-011-9223-1
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    References listed on IDEAS

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    1. 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.
    2. Frank B. Knight, 2000. "The moments of the area under reflected Brownian bridge conditional on its local time at zero," International Journal of Stochastic Analysis, Hindawi, vol. 13, pages 1-26, January.
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    Cited by:

    1. Mario Abundo & Danilo Del Vescovo, 2017. "On the Joint Distribution of First-passage Time and First-passage Area of Drifted Brownian Motion," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 985-996, September.

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