Abstract
We consider the first-crossing-time problem through a constant boundary
for a Wiener process perturbed by random jumps driven by a counting process. On the
base of a sample-path analysis of the jump-diffusion process we obtain explicit lower
bounds for the first-crossing-time density and for the first-crossing-time distribution
function. In the case of the distribution function, the bound is improved by use of
processes comparison based on the usual stochastic order. The special case of constant
jumps driven by a Poisson process is thoroughly discussed.
