Regularity of the optimal stopping problem for jump diffusions. (English) Zbl 1255.60068
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 Lévy measure, this paper shows that the value function of this optimal stopping problem on an unbounded domain with finite/infinite variation jumps is in \(W^{2,1}_{p,\mathrm{loc}}\) with \(p\in(1, \infty)\). As a consequence, the smooth-fit property holds.
Reviewer: Pavel Gapeev (London)
MSC:
60G40 | Stopping times; optimal stopping problems; gambling theory |
60J75 | Jump processes (MSC2010) |
35R35 | Free boundary problems for PDEs |
45K05 | Integro-partial differential equations |