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A Stochastic Approximation for Fully Nonlinear Free Boundary Parabolic Problems

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  • Erhan Bayraktar
  • Arash Fahim

Abstract

We present a stochastic numerical method for solving fully non-linear free boundary problems of parabolic type and provide a rate of convergence under reasonable conditions on the non-linearity.

Suggested Citation

  • Erhan Bayraktar & Arash Fahim, 2011. "A Stochastic Approximation for Fully Nonlinear Free Boundary Parabolic Problems," Papers 1109.5752, arXiv.org, revised Nov 2013.
    • Handle: RePEc:arx:papers:1109.5752
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    File URL: http://arxiv.org/pdf/1109.5752
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    References listed on IDEAS

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    1. A. Oberman & T. Zariphopoulou, 2003. "Pricing early exercise contracts in incomplete markets," Computational Management Science, Springer, vol. 1(1), pages 75-107, December.
    2. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
    3. Ma, Jin & Zhang, Jianfeng, 2005. "Representations and regularities for solutions to BSDEs with reflections," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 539-569, April.
    4. Erhan Bayraktar & Yu-Jui Huang, 2010. "On the Multi-Dimensional Controller and Stopper Games," Papers 1009.0932, arXiv.org, revised Jan 2013.
    5. repec:dau:papers:123456789/5524 is not listed on IDEAS
    6. Ioannis Karatzas & (*), S. G. Kou, 1998. "Hedging American contingent claims with constrained portfolios," Finance and Stochastics, Springer, vol. 2(3), pages 215-258.
    7. repec:cdl:anderf:qt43n1k4jb is not listed on IDEAS
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    Cited by:

    1. Arash Fahim & Wan-Yu Tsai, 2017. "A Numerical Scheme for A Singular control problem: Investment-Consumption Under Proportional Transaction Costs," Papers 1711.01017, arXiv.org.

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