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One-dimensional BSDEs with left-continuous, lower semi-continuous and linear-growth generators

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  • Fan, ShengJun
  • Jiang, Long

Abstract

This paper deals with a one-dimensional backward stochastic differential equation (BSDE) whose generator g is of linear growth in (y,z), left-continuous and lower semi-continuous (maybe discontinuous) in y, and continuous in z. We establish, in this setting, the existence of the minimal solution to the BSDE. And we also prove a comparison theorem and a Levi type theorem for the minimal solutions. They generalize some known results.

Suggested Citation

  • Fan, ShengJun & Jiang, Long, 2012. "One-dimensional BSDEs with left-continuous, lower semi-continuous and linear-growth generators," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1792-1798.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:10:p:1792-1798
    DOI: 10.1016/j.spl.2012.06.004
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    References listed on IDEAS

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    1. Jia, Guangyan, 2008. "A class of backward stochastic differential equations with discontinuous coefficients," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 231-237, February.
    2. 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.
    3. 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.
    4. Liu, Jicheng & Ren, Jiagang, 2002. "Comparison theorem for solutions of backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 56(1), pages 93-100, January.
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    Cited by:

    1. Fan, ShengJun, 2016. "Existence of solutions to one-dimensional BSDEs with semi-linear growth and general growth generators," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 7-15.
    2. Hamadène, Said & Mu, Rui, 2020. "Discontinuous Nash equilibrium points for nonzero-sum stochastic differential games," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6901-6926.

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