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First-passage problems for diffusion processes with state-dependent jumps

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  • Mario Lefebvre

Abstract

Let X(t) be a time-homogeneous jump-diffusion process. We assume that the jump size depends on the value of X(t). We obtain analytical results for the moments of T(x) and of X(T(x)), where T(x) is the first time that the process leaves the interval (a, b). We also compute P[X(T(x))≤a]. These results have applications in financial mathematics.

Suggested Citation

  • Mario Lefebvre, 2022. "First-passage problems for diffusion processes with state-dependent jumps," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(9), pages 2908-2918, March.
    • Handle: RePEc:taf:lstaxx:v:51:y:2022:i:9:p:2908-2918
    DOI: 10.1080/03610926.2020.1784433
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