Regularity of the Optimal Stopping Problem for Jump Diffusions

Details Regularity of the Optimal Stopping Problem for Jump Diffusions Regularity of the Optimal Stopping Problem for Jump Diffusions

2009-02-15

arxiv.org/abs/0902.2479v6

Mathematics

Optimization and Control

To Appear in the SIAM Journal on Control and Optimization

Scientific paper

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.

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