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Regularity of the Optimal Stopping Problem for Jump Diffusions

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  • Erhan Bayraktar
  • Hao Xing

Abstract

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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File URL: http://arxiv.org/pdf/0902.2479
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 0902.2479.

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Date of creation: Feb 2009
Date of revision: Mar 2012
Handle: RePEc:arx:papers:0902.2479

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Web page: http://arxiv.org/

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