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Bounded solutions, Lp(p>1) solutions and L1 solutions for one dimensional BSDEs under general assumptions

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  • Fan, ShengJun

Abstract

This paper aims at solving one dimensional backward stochastic differential equations (BSDEs) under weaker assumptions. We establish general existence, uniqueness, and comparison results for bounded solutions, Lp(p>1) solutions and L1 solutions of the BSDEs. The time horizon is allowed to be finite or infinite, and the generator g is allowed to have a general growth in y and a quadratic growth in z. As compensation, the generator g needs to satisfy a kind of one-sided linear or super-linear growth condition in y, instead of the monotonicity condition in y as is usually done. Many of our results improve considerably some known results, even though for the case of finite time horizon and the case of L2 solution.

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  • 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.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:5:p:1511-1552
    DOI: 10.1016/j.spa.2015.11.012
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    References listed on IDEAS

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    9. 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. Joshua Aurand & Yu-Jui Huang, 2020. "Mortality and Healthcare: a Stochastic Control Analysis under Epstein-Zin Preferences," Papers 2003.01783, arXiv.org, revised Jul 2021.
    2. Fan, Shengjun & Hu, Ying, 2021. "Well-posedness of scalar BSDEs with sub-quadratic generators and related PDEs," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 21-50.
    3. Kim, Kon-Gun & Kim, Mun-Chol & O, Hun, 2022. "Local existence and uniqueness of solutions to quadratic BSDEs with weak monotonicity and general growth generators," Statistics & Probability Letters, Elsevier, vol. 186(C).
    4. 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.
    5. Antonis Papapantoleon & Dylan Possamai & Alexandros Saplaouras, 2016. "Existence and uniqueness results for BSDEs with jumps: the whole nine yards," Papers 1607.04214, arXiv.org, revised Nov 2018.

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