Quadratic reflected BSDEs with unbounded obstacles
AbstractIn 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, uniqueness, 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 concave in the z-variable.
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Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 122 (2012)
Issue (Month): 4 ()
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
Other versions of this item:
- Erhan Bayraktar & Song Yao, 2010. "Quadratic Reflected BSDEs with Unbounded Obstacles," Papers 1005.3565, arXiv.org, revised Mar 2011.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Bayraktar, Erhan & Yao, Song, 2011.
"Optimal stopping for non-linear expectations--Part I,"
Stochastic Processes and their Applications,
Elsevier, vol. 121(2), pages 185-211, February.
- Bayraktar, Erhan & Yao, Song, 2011. "Optimal stopping for non-linear expectations--Part II," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 212-264, February.
- Matoussi, Anis, 1997. "Reflected solutions of backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 347-354, June.
- N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71.
- Lepeltier, J. P. & San Martin, J., 1997. "Backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 425-430, April.
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