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Quadratic Reflected BSDEs with Unbounded Obstacles

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  • Erhan Bayraktar
  • Song Yao

Abstract

In this paper, we analyze a real-valued reflected backward stochastic differential equation (RBSDE) with an unbounded obstacle and an unbounded terminal condition when its generator $f$ has quadratic growth in the $z$-variable. In particular, we obtain existence, comparison, and stability results, and consider the optimal stopping for quadratic $g$-evaluations. As an application of our results we analyze the obstacle problem for semi-linear parabolic PDEs in which the non-linearity appears as the square of the gradient. Finally, we prove a comparison theorem for these obstacle problems when the generator is convex or concave in the $z$-variable.

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File URL: http://arxiv.org/pdf/1005.3565
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Paper provided by arXiv.org in its series Papers with number 1005.3565.

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Date of creation: May 2010
Date of revision: Mar 2011
Handle: RePEc:arx:papers:1005.3565

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  1. Bayraktar, Erhan & Yao, Song, 2011. "Optimal stopping for non-linear expectations--Part I," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 121(2), pages 185-211, February.
  2. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 7(1), pages 1-71.
  3. Matoussi, Anis, 1997. "Reflected solutions of backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, Elsevier, vol. 34(4), pages 347-354, June.
  4. Lepeltier, J. P. & San Martin, J., 1997. "Backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, Elsevier, vol. 32(4), pages 425-430, April.
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Cited by:
  1. Lionnet, Arnaud, 2014. "Some results on general quadratic reflected BSDEs driven by a continuous martingale," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 124(3), pages 1275-1302.

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