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Peer-reviewedCC BY 4.0Axioms

First-Passage Time Problems for Jump-Diffusion Processes with Positive and Negative Jumps

  • Mario Lefebvre1
  • Antoine Habib1
  1. 1Department of Mathematics and Industrial Engineering, Polytechnique Montréal, Succursale Centre-Ville, P.O. Box 6079, Montréal, QC H3C 3A7, Canada
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Abstract

Let τ(x) be the first time that a jump-diffusion process with positive and negative jumps leaves the interval (a,b). The moment-generating function M(x) of τ(x) satisfies an integro-differential equation (IDE). In the case of exponential jumps, we transform this IDE into an ordinary differential equation (ODE). This is similar to the IDE satisfied by m(x):=E[τ(x)]. Explicit solutions to particular problems are obtained for both M(x) and m(x) by solving the appropriate ODEs.

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Cite

BibTeXRIS
BibTeX
@article{lefebvre2026firstpassage,
  title = {{First-Passage Time Problems for Jump-Diffusion Processes with Positive and Negative Jumps}},
  author = {Mario Lefebvre and Antoine Habib},
  journal = {Axioms},
  year = {2026},
  month = oct,
  doi = {10.3390/axioms15100734},
  url = {https://www.mdpi.com/2075-1680/15/10/734},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - First-Passage Time Problems for Jump-Diffusion Processes with Positive and Negative Jumps
AU  - Mario Lefebvre
AU  - Antoine Habib
PY  - 2026
DA  - 2026/10/01
JO  - Axioms
DO  - 10.3390/axioms15100734
UR  - https://www.mdpi.com/2075-1680/15/10/734
AB  - Let τ(x) be the first time that a jump-diffusion process with positive and negative jumps leaves the interval (a,b). The moment-generating function M(x) of τ(x) satisfies an integro-differential equation (IDE). In the case of exponential jumps, we transform this IDE into an ordinary differential equation (ODE). This is similar to the IDE satisfied by m(x):=E[τ(x)]. Explicit solutions to particular problems are obtained for both M(x) and m(x) by solving the appropriate ODEs.
SN  - 2075-1680
ER  -