The value function of an optimal stopping problem for a process with Levy jumps is known to be a generalized solution of a variational inequality. Assuming the diffusion component of the process is non-degenerate and a mild assumption on the singularity of the Levy measure, this paper shows that the value function is smooth in the continuation region for problems with either finite or infinite variation jumps . Moreover , the smooth-fit property is shown via the global regularity of the value function .
The value function of an optimal stopping problem for a process with L\'{e jumps 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 measure, this paper shows that the value function of problems on an unbounded domain with infinite activity jumps is W^{2,1 , the smooth-fit property holds and the value function is C^{2,1 .
R
Levy
L\'{e
R
non-degenerate
nondegenerate
R
Levy
L\'{e
R
is smooth in the continuation region for problems with either finite or infinite variation jumps . Moreover
of problems on an unbounded domain with infinite activity jumps is W^{2,1
R
is shown via the global regularity of the value function
holds and the value function is C^{2,1