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The Wiener disorder problem with finite horizon

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  • Gapeev, P.V.
  • Peskir, G.

Abstract

The Wiener disorder problem seeks to determine a stopping time which is as close as possible to the (unknown) time of 'disorder' when the drift of an observed Wiener process changes from one value to another. In this paper we present a solution of the Wiener disorder problem when the horizon is finite. The method of proof is based on reducing the initial problem to a parabolic free-boundary problem where the continuation region is determined by a continuous curved boundary. By means of the change-of-variable formula containing the local time of a diffusion process on curves we show that the optimal boundary can be characterized as a unique solution of the nonlinear integral equation.

Suggested Citation

  • Gapeev, P.V. & Peskir, G., 2006. "The Wiener disorder problem with finite horizon," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1770-1791, December.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:12:p:1770-1791
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    References listed on IDEAS

    as
    1. Goran Peskir, 2005. "On The American Option Problem," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 169-181, January.
    2. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14, April.
    3. Goran Peskir, 2005. "The Russian option: Finite horizon," Finance and Stochastics, Springer, vol. 9(2), pages 251-267, April.
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