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On first-passage times for one-dimensional jump-diffusion processes

Abundo M.

Probability and Mathematical Statistics

2000

Vol. 20, Fasc. 2

399--423

Some problems of first-crossing times over two time-dependent boundaries for one-dimensional jump-diffusion processes are considered. The moments of the first-crossing times over each boundary are shown to be the solutions of certain partial differential-difference equations with suitable outer conditions. An approach based on the Laplace transform allows us to compare the moments of the first-crossing times of the jump-diffusion process with those of the corresponding simple-diffusion without jumps. For some examples where the boundaries are constant, the results are illustrated graphically.