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Some uniqueness results for one-dimensional BSDEs with uniformly continuous coefficients

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  • Jia, Guangyan

Abstract

In this note we discuss one-dimensional backward stochastic differential equations (BSDEs) with coefficient g which is uniformly continuous in (y,z). As we know, the solution to this kind of BSDE may be non-unique. We prove that, the set of real numbers c such that the solution of perturbed BSDE with coefficient g+c is non-unique, is at most countable, and we give some necessary and sufficient conditions for the uniqueness for solution to this kind of BSDEs. More importantly, we prove that if g is independent of y, the solution of corresponding BSDE is unique.

Suggested Citation

  • Jia, Guangyan, 2009. "Some uniqueness results for one-dimensional BSDEs with uniformly continuous coefficients," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 436-441, February.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:4:p:436-441
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    1. 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.
    2. 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.
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    1. Tu, Shuheng & Hao, Wu & Chen, Jing, 2017. "The adapted solutions and comparison theorem for anticipated backward stochastic differential equations with Poisson jumps under the weak conditions," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 7-17.

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