ON FIRST-PASSAGE TIMES FOR ONE-DIMENSIONAL JUMP-DIFFUSION
PROCESSES
Abstract: 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.
1991 AMS Mathematics Subject Classification: Primary 60J60; Secondary 60J99;
60H10.
Key words and phrases: Jump-diffusion process, exit probability, first-crossing time.