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On a Solution of the Optimal Stopping Problem for Processes with Independent Increments

  • Alexander Novikov

    (Department of Mathematics, University of Technology, Sydney)

  • Albert Shiryaev

    (Mathematical Institute, Moscow, Russia)

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    We discuss a solution of the optimal stopping problem for the case when a reward function is a power function of a process with independent stationary increments (random walks or Levy processes) on an infinite time interval. It is shown that an optimal stopping time is the first crossing time through a level defined as the largest root of the Appell function associated with the maximum of the underlying process.

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    File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp178.pdf
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    Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 178.

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    Length: 15 pages
    Date of creation: 01 Jun 2006
    Date of revision:
    Publication status: Published as: Novikov, A. and Shiryaev, A, 2007, "On a Solution of the Optimal Stopping Problem for Processes with Independent Increments", Stochastics An International Journal of Probability and Stochastic Processes, 79(3-4), 393-406.
    Handle: RePEc:uts:rpaper:178
    Contact details of provider: Postal:
    PO Box 123, Broadway, NSW 2007, Australia

    Phone: +61 2 9514 7777
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    Web page: http://www.qfrc.uts.edu.au/

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    1. Alexander Novikov & Albert Shiryaev, 2004. "On an Effective Solution of the Optimal Stopping Problem for Random Walks," Research Paper Series 131, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Ernesto Mordecki, 2002. "Optimal stopping and perpetual options for Lévy processes," Finance and Stochastics, Springer, vol. 6(4), pages 473-493.
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