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An iteration procedure for solving integral equations related to optimal stopping problems

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  • Belomestny, Denis
  • Gapeev, Pavel V.

Abstract

A new algorithm for finding value functions of finite horizon optimal stopping problems in one-dimensional diffusion models is presented. It is based on a time discretization of the corresponding integral equation. The proposed iterative procedure for solving the discretized integral equation converges in a finite number of steps and delivers in each step a lower or an upper bound for value of discretized problem on the whole time interval. The remarks on the application of the method for solving integral equations related to some optimal stopping problems are given.

Suggested Citation

  • Belomestny, Denis & Gapeev, Pavel V., 2006. "An iteration procedure for solving integral equations related to optimal stopping problems," SFB 649 Discussion Papers 2006-043, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2006-043
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    References listed on IDEAS

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    1. Goran Peskir, 2005. "A Change-of-Variable Formula with Local Time on Curves," Journal of Theoretical Probability, Springer, vol. 18(3), pages 499-535, July.
    2. Belomestny, Denis & Gapeev, Pavel V., 2006. "An iteration procedure for solving integral equations related to optimal stopping problems," SFB 649 Discussion Papers 2006-043, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
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    1. Belomestny, Denis & Gapeev, Pavel V., 2006. "An iteration procedure for solving integral equations related to optimal stopping problems," SFB 649 Discussion Papers 2006-043, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.

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