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Limit theorem and uniqueness theorem of backward stochastic differential equations

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Abstract

This paper establishes a limit theorem for solutions of backward stochastic differential equations (BSDEs). By this limit theorem, this paper proves that, under the standard assumption g(t,y,0) ≡ 0, the generator g of a BSDE can be uniquely determined by the corresponding g-expectation ɛ g; this paper also proves that if a filtration consistent expectation ɛ can be represented as a g-expectation ɛ g, then the corresponding generator g must be unique.

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Authors and Affiliations

  1. Department of Mathematics, China University of Mining and Technology, Xuzhou, 221008, China

    Jiang Long

  2. Institute of Mathematics, Fudan University, Shanghai, 200433, China

    Jiang Long

  3. School of Mathematics and System Sciences, Shandong University, Jinan, 250100, China

    Jiang Long

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  1. Jiang Long
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Jiang, L. Limit theorem and uniqueness theorem of backward stochastic differential equations. SCI CHINA SER A 49, 1353–1362 (2006). https://doi.org/10.1007/s11425-006-2024-2

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  • DOI: https://doi.org/10.1007/s11425-006-2024-2

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