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Lp solutions of reflected BSDEs under monotonicity condition

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  • Rozkosz, Andrzej
  • Słomiński, Leszek

Abstract

We prove existence and uniqueness of Lp solutions, p∈[1,2], of reflected backward stochastic differential equations with p-integrable data and generators satisfying the monotonicity condition. We also show that the solution may be approximated by the penalization method. Our results are new even in the classical case p=2.

Suggested Citation

  • Rozkosz, Andrzej & Słomiński, Leszek, 2012. "Lp solutions of reflected BSDEs under monotonicity condition," Stochastic Processes and their Applications, Elsevier, vol. 122(12), pages 3875-3900.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:12:p:3875-3900
    DOI: 10.1016/j.spa.2012.07.006
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    References listed on IDEAS

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    1. 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.
    2. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
    3. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    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. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
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    Cited by:

    1. Falkowski, Adrian & Słomiński, Leszek, 2020. "Backward stochastic differential equations with two barriers and generalized reflection," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4746-4765.
    2. Klimsiak, Tomasz & Rzymowski, Maurycy & Słomiński, Leszek, 2019. "Reflected BSDEs with regulated trajectories," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1153-1184.
    3. Klimsiak, Tomasz, 2015. "Reflected BSDEs on filtered probability spaces," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4204-4241.
    4. Klimsiak, Tomasz & Rozkosz, Andrzej & Słomiński, Leszek, 2015. "Reflected BSDEs in time-dependent convex regions," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 571-596.
    5. Klimsiak, Tomasz, 2021. "Non-semimartingale solutions of reflected BSDEs and applications to Dynkin games," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 208-239.
    6. Kim, Mun-Chol & O, Hun, 2021. "A general comparison theorem for reflected BSDEs," Statistics & Probability Letters, Elsevier, vol. 173(C).
    7. Bensoussan, Alain & Li, Yiqun & Yam, Sheung Chi Phillip, 2018. "Backward stochastic dynamics with a subdifferential operator and non-local parabolic variational inequalities," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 644-688.

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