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One-dimensional BSDEs with finite and infinite time horizons

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  • Fan, ShengJun
  • Jiang, Long
  • Tian, DeJian

Abstract

This paper is devoted to solving one-dimensional backward stochastic differential equations (BSDEs), where the time horizon may be finite or infinite and the assumptions on the generator g are not necessary to be uniform on t. We first show the existence of the minimal solution for this kind of BSDEs with linear growth generators. Then, we establish a general comparison theorem for solutions of this kind of BSDEs with weakly monotonic and uniformly continuous generators. Finally, we give an existence and uniqueness result for solutions of this kind of BSDEs with uniformly continuous generators.

Suggested Citation

  • Fan, ShengJun & Jiang, Long & Tian, DeJian, 2011. "One-dimensional BSDEs with finite and infinite time horizons," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 427-440, March.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:3:p:427-440
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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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    Cited by:

    1. Sheng Jun Fan, 2018. "Existence, Uniqueness and Stability of $$L^1$$ L 1 Solutions for Multidimensional Backward Stochastic Differential Equations with Generators of One-Sided Osgood Type," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1860-1899, September.
    2. Zhang, HengMin & Fan, ShengJun, 2013. "A representation theorem for generators of BSDEs with finite or infinite time intervals and linear-growth generators," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 724-734.
    3. Han, Jinhui & Li, Xiaolong & Ma, Guiyuan & Kennedy, Adrian Patrick, 2023. "Strategic trading with information acquisition and long-memory stochastic liquidity," European Journal of Operational Research, Elsevier, vol. 308(1), pages 480-495.
    4. Falei Wang & Guoqiang Zheng, 2021. "Backward Stochastic Differential Equations Driven by G-Brownian Motion with Uniformly Continuous Generators," Journal of Theoretical Probability, Springer, vol. 34(2), pages 660-681, June.
    5. Tian, Dejian & Jiang, Long & Shi, Xuejun, 2013. "Lp solutions to backward stochastic differential equations with discontinuous generators," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 503-510.
    6. Fan, ShengJun, 2016. "Bounded solutions, Lp(p>1) solutions and L1 solutions for one dimensional BSDEs under general assumptions," Stochastic Processes and their Applications, Elsevier, vol. 126(5), pages 1511-1552.

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