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Existence of solutions to one-dimensional BSDEs with semi-linear growth and general growth generators

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  • Fan, ShengJun

Abstract

This paper is devoted to solving a one-dimensional backward stochastic differential equation (BSDE in short) when the generator g has a semi-linear growth and a general growth in (y,z). This condition is not only strictly weaker than the linear growth condition of g in (y,z), but also the (weak) monotonicity and general growth condition of g in y together with the linear growth condition of g in z. We establish, in this setting, three existence results on a solution and the minimal (maximal) solution to the BSDE, where the generator g may be discontinuous in y. These results virtually unify and improve some existing results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:109:y:2016:i:c:p:7-15
    DOI: 10.1016/j.spl.2015.10.012
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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.
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    3. 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.
    4. Briand, Ph. & Delyon, B. & Hu, Y. & Pardoux, E. & Stoica, L., 2003. "Lp solutions of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 109-129, November.
    5. Mao, Xuerong, 1995. "Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 281-292, August.
    6. 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.
    7. 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.
    8. Jia, Guangyan, 2010. "Backward stochastic differential equations with a uniformly continuous generator and related g-expectation," Stochastic Processes and their Applications, Elsevier, vol. 120(11), pages 2241-2257, November.
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    Cited by:

    1. Fan, Shengjun & Hu, Ying & Tang, Shanjian, 2023. "Existence, uniqueness and comparison theorem on unbounded solutions of scalar super-linear BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 335-375.

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