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Reflected BSDE with a Constraint and a New Doob-Meyer Nonlinear Decomposition

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  • Shige Peng
  • Mingyu Xu

Abstract

In this paper, we study a type of reflected BSDE with a constraint and introduce a new kind of nonlinear expectation via BSDE with a constraint and prove the Doob-Meyer decomposition with respect to the super(sub)martingale introduced by this nonlinear expectation. We then apply the results to the pricing of American options in incomplete market.

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  • Shige Peng & Mingyu Xu, 2006. "Reflected BSDE with a Constraint and a New Doob-Meyer Nonlinear Decomposition," Papers math/0611869, arXiv.org, revised Jul 2008.
    • Handle: RePEc:arx:papers:math/0611869
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    References listed on IDEAS

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    1. 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, January.
    2. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    3. Lepeltier, J.-P. & Xu, M., 2005. "Penalization method for reflected backward stochastic differential equations with one r.c.l.l. barrier," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 58-66, November.
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