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A note on optional Snell envelopes and reflected backward SDEs

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  • Marzougue, Mohamed

Abstract

In this note we introduce a notion of optional Snell envelopes over the so-called split stopping times. As application, we give a solution to reflected backward stochastic differential equations when the barrier is an optional positive process neither right-continuous nor left-continuous.

Suggested Citation

  • Marzougue, Mohamed, 2020. "A note on optional Snell envelopes and reflected backward SDEs," Statistics & Probability Letters, Elsevier, vol. 165(C).
    • Handle: RePEc:eee:stapro:v:165:y:2020:i:c:s016771522030136x
    DOI: 10.1016/j.spl.2020.108833
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    References listed on IDEAS

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    1. Miryana Grigorova & Peter Imkeller & Elias Offen & Youssef Ouknine & Marie-Claire Quenez, 2017. "Reflected BSDEs when the obstacle is not right-continuous and optimal stopping," Post-Print hal-01141801, HAL.
    2. Miryana Grigorova & Peter Imkeller & Youssef Ouknine & Marie-Claire Quenez, 2018. "Doubly Reflected BSDEs and ${\cal E}^{f}$-Dynkin games: beyond the right-continuous case," Working Papers hal-01497914, HAL.
    3. Miryana Grigorova & Peter Imkeller & Elias Offen & Youssef Ouknine & Marie-Claire Quenez, 2015. "Reflected BSDEs when the obstacle is not right-continuous and optimal stopping," Papers 1504.06094, arXiv.org, revised May 2017.
    4. Grigorova, Miryana & Imkeller, Peter & Quenez, Marie-Claire & Ouknine, Youssef, 2018. "Doubly Reflected BSDEs and $\mathcal{E}$$^ƒ$-Dynkin games: beyond the right-continuous case," Center for Mathematical Economics Working Papers 598, Center for Mathematical Economics, Bielefeld University.
    5. Klimsiak, Tomasz & Rzymowski, Maurycy & Słomiński, Leszek, 2019. "Reflected BSDEs with regulated trajectories," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1153-1184.
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    Cited by:

    1. Marzougue, Mohamed, 2021. "Monotonic limit theorem for BSDEs with regulated trajectories," Statistics & Probability Letters, Elsevier, vol. 176(C).
    2. Marzougue, Mohamed, 2023. "Non-linear Dynkin games over split stopping times," Statistics & Probability Letters, Elsevier, vol. 193(C).

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