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$${{\varvec{L}}}^{{\varvec{p}}}$$ L p -Solutions and Comparison Results for Lévy-Driven Backward Stochastic Differential Equations in a Monotonic, General Growth Setting

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  • Stefan Kremsner

    (University of Graz)

  • Alexander Steinicke

    (Montanuniversitaet Leoben)

Abstract

We present a unified approach to $$L^p$$ L p -solutions ( $$p > 1$$ p > 1 ) of multidimensional backward stochastic differential equations (BSDEs) driven by Lévy processes and more general filtrations. New existence, uniqueness and comparison results are obtained. The generator functions obey a time-dependent extended monotonicity (Osgood) condition in the y-variable and have general growth in y. Within this setting, the results generalize those of Royer, Yin and Mao, Yao, Kruse and Popier, and Geiss and Steinicke.

Suggested Citation

  • Stefan Kremsner & Alexander Steinicke, 2022. "$${{\varvec{L}}}^{{\varvec{p}}}$$ L p -Solutions and Comparison Results for Lévy-Driven Backward Stochastic Differential Equations in a Monotonic, General Growth Setting," Journal of Theoretical Probability, Springer, vol. 35(1), pages 231-281, March.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:1:d:10.1007_s10959-020-01056-3
    DOI: 10.1007/s10959-020-01056-3
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    References listed on IDEAS

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    1. Fujii, Masaaki & Takahashi, Akihiko, 2018. "Quadratic–exponential growth BSDEs with jumps and their Malliavin’s differentiability," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 2083-2130.
    2. Philippe Briand & René Carmona, 2000. "BSDEs with polynomial growth generators," International Journal of Stochastic Analysis, Hindawi, vol. 13, pages 1-32, January.
    3. 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.
    4. Yao, Song, 2017. "Lp solutions of backward stochastic differential equations with jumps," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3465-3511.
    5. 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.
    6. Alexander Steinicke, 2016. "Functionals of a Lévy Process on Canonical and Generic Probability Spaces," Journal of Theoretical Probability, Springer, vol. 29(2), pages 443-458, June.
    7. Royer, Manuela, 2006. "Backward stochastic differential equations with jumps and related non-linear expectations," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1358-1376, October.
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