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On an Inverse First-Passage Problem for Jump-Diffusion Processes

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  • Mario Lefebvre

    (Department of Mathematics and Industrial Engineering, Polytechnique Montreal, P.O. Box 6079, Succursale Centre-Ville, Montreal, QC H3C 3A7, Canada)

Abstract

Computing the exact mathematical expression for a quantity defined in terms of a first-passage time random variable for a jump-diffusion process is in general very difficult. In this paper, we consider the following inverse problem: can we find a certain distribution for the size of the jumps that leads to a simple solution of the integro-differential equation satisfied by the quantity of interest, subject to the appropriate boundary conditions? Such distributions are found, in particular, for the mean of the first-passage time for important jump-diffusion processes.

Suggested Citation

  • Mario Lefebvre, 2025. "On an Inverse First-Passage Problem for Jump-Diffusion Processes," Mathematics, MDPI, vol. 14(1), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:14:y:2025:i:1:p:87-:d:1827002
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