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

Mario Abundo ()
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Mario Abundo: Università “Tor Vergata”

Methodology and Computing in Applied Probability, 2013, vol. 15, issue 1, 85-103

Abstract: 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.

Keywords: First-passage time; First-passage area; One-dimensional jump-diffusion; 60J60; 60H05; 60H10 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s11009-011-9223-1

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