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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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  • Erhan Bayraktar & Hao Xing, 2009. "Regularity of the Optimal Stopping Problem for Jump Diffusions," Papers 0902.2479, arXiv.org, revised Mar 2012.
    • Handle: RePEc:arx:papers:0902.2479
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    Cited by:

    1. Keller, Godfrey & Rady, Sven, 2015. "Breakdowns," Theoretical Economics, Econometric Society, vol. 10(1), January.
    2. Baurdoux, Erik J. & Pedraza, José M., 2024. "Lp optimal prediction of the last zero of a spectrally negative Lévy process," LSE Research Online Documents on Economics 119468, London School of Economics and Political Science, LSE Library.

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