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A Class of Solvable Optimal Stopping Problems of Spectrally Negative Jump Diffusions

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  • Luis H. R. Alvarez

    ()
    (Department of Economics, Turku School of Economics)

  • Teppo A. Rakkolainen

    ()
    (Department of Economics, Turku School of Economics)

Abstract

We consider the optimal stopping of a class of spectrally negative jump diffusions. We state a set of conditions under which the value is shown to have a representation in terms of an ordinary nonlinear programming problem. We establish a connection between the considered problem and a stopping problem of an associated continuous diffusion process and demonstrate how this connection may be applied for characterizing the stopping policy and its value. We also establish a set of typically satisfied conditions under which increased volatility as well as higher jump-intensity decelerates rational exercise by increasing the value and expanding the continuation region.

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Bibliographic Info

Paper provided by Aboa Centre for Economics in its series Discussion Papers with number 9.

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Length: 46
Date of creation: Oct 2006
Date of revision:
Handle: RePEc:tkk:dpaper:dp9

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Keywords: jump diffusions; optimal stopping; nonlinear programming; perpetual American options;

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References

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  1. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
  2. Boyarchenko, Svetlana & Levendorskii[caron], Sergei, 2007. "Optimal stopping made easy," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 201-217, February.
  3. Luis Alvarez, 1996. "Demand uncertainty and the value of supply opportunities," Journal of Economics, Springer, vol. 64(2), pages 163-175, June.
  4. Bernanke, Ben S, 1983. "Irreversibility, Uncertainty, and Cyclical Investment," The Quarterly Journal of Economics, MIT Press, vol. 98(1), pages 85-106, February.
  5. Svetlana Boyarchenko, 2004. "Irreversible Decisions and Record-Setting News Principles," American Economic Review, American Economic Association, vol. 94(3), pages 557-568, June.
  6. Svetlana Boyarchenko & Sergei Levendorskii, 2004. "American options: the EPV pricing model," Finance 0405024, EconWPA.
  7. Ernesto Mordecki, 2002. "Optimal stopping and perpetual options for Lévy processes," Finance and Stochastics, Springer, vol. 6(4), pages 473-493.
  8. Luis H. R. Alvarez, 2001. "Reward functionals, salvage values, and optimal stopping," Computational Statistics, Springer, vol. 54(2), pages 315-337, December.
  9. Luis Alvarez & Teppo Rakkolainen, 2010. "Investment timing in presence of downside risk: a certainty equivalent characterization," Annals of Finance, Springer, vol. 6(3), pages 317-333, July.
  10. L. Alili & A. E. Kyprianou, 2005. "Some remarks on first passage of Levy processes, the American put and pasting principles," Papers math/0508487, arXiv.org.
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Citations

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Cited by:
  1. Luis Alvarez & Teppo Rakkolainen, 2010. "Investment timing in presence of downside risk: a certainty equivalent characterization," Annals of Finance, Springer, vol. 6(3), pages 317-333, July.
  2. Luis H. R. Alvarez & Teppo A. Rakkolainen, 2007. "Optimal Dividend Control in Presence of Downside Risk," Discussion Papers 14, Aboa Centre for Economics.
  3. Masahiko Egami & Mingxin Xu, 2009. "A continuous-time search model with job switch and jumps," Computational Statistics, Springer, vol. 70(2), pages 241-267, October.

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