  We present an analytic solution of a differential-difference equation that
appears when one solves an optimal stopping time problem with state process
following a jump-diffusion process.
  This equation occurs in the context of real options and finance options, for
instance, when one derives the optimal time to undertake a decision. Due to the
jump process, the equation is not local in the boundary set. The solution that
we present - which takes into account the geometry of the problem - is written
in a backward form, and therefore its analysis (along with its implementation)
is easy to follow.
