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Reflected BSDEs with regulated trajectories

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  • Klimsiak, Tomasz
  • Rzymowski, Maurycy
  • Słomiński, Leszek

Abstract

We consider reflected backward stochastic different equations with optional barrier and so-called regulated trajectories, i.e. trajectories with left and right finite limits. We prove existence and uniqueness results. We also show that the solution corresponds to the value of an optimal stopping problem and may be approximated by a modified penalization method.

Suggested Citation

  • Klimsiak, Tomasz & Rzymowski, Maurycy & Słomiński, Leszek, 2019. "Reflected BSDEs with regulated trajectories," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1153-1184.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:4:p:1153-1184
    DOI: 10.1016/j.spa.2018.04.011
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    References listed on IDEAS

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    1. Lepeltier, J.-P. & Xu, M., 2005. "Penalization method for reflected backward stochastic differential equations with one r.c.l.l. barrier," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 58-66, November.
    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. 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.
    4. 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.
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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. Marzougue, Mohamed, 2020. "A note on optional Snell envelopes and reflected backward SDEs," Statistics & Probability Letters, Elsevier, vol. 165(C).
    3. Marzougue, Mohamed, 2021. "Monotonic limit theorem for BSDEs with regulated trajectories," Statistics & Probability Letters, Elsevier, vol. 176(C).
    4. Grigorova, Miryana & Imkeller, Peter & Ouknine, Youssef & Quenez, Marie-Claire, 2020. "Optimal stopping with f-expectations: The irregular case," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1258-1288.
    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. Imane Jarni & Youssef Ouknine, 2021. "On Reflection with Two-Sided Jumps," Journal of Theoretical Probability, Springer, vol. 34(4), pages 1811-1830, December.

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