The value function of an optimal stopping problem for a process with L\'{e is known to be a generalized solution of a variational inequality. Assuming  the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of obstacle problems on an unbounded domain with finite/infinite variation jumps is in W^{2,1}_{p, loc}  . As a consequence, the smooth-fit property holds.
The value function of an optimal stopping problem for jump diffusions is known to be a generalized solution of a variational inequality. Assuming that the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the L\'{e}vy measure, this paper shows that the value function of this optimal stopping problem on an unbounded domain with finite/infinite variation jumps is in W^{2,1}_{p, loc} with p\in(1, \infty) . As a consequence, the smooth-fit property holds.
R
a process with L\'{e
jump diffusions
A
that
R
obstacle problems
this optimal stopping problem
A
with p\in(1, \infty)