Regularity of the optimal stopping problem for jump diffusions (Q2910907)
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scientific article; zbMATH DE number 6081255
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Regularity of the optimal stopping problem for jump diffusions |
scientific article; zbMATH DE number 6081255 |
Statements
12 September 2012
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optimal stopping
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variational inequality
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Lévy process
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regularity of the value function
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smooth-fit principle
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Sobolev spaces
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Regularity of the optimal stopping problem for jump diffusions (English)
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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.
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