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Optimal stopping with f -expectations: the irregular case

Author

Listed:
  • Miryana Grigorova

    (Universität Bielefeld)

  • Peter Imkeller

    (Institut für Mathematik [Berlin] - TU - Technical University of Berlin / Technische Universität Berlin)

  • Youssef Ouknine

    (Faculté des Sciences Semlalia [Marrakech] - UCA - Université Cadi Ayyad [Marrakech])

  • Marie-Claire Quenez

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité)

Abstract

We consider the optimal stopping problem with non-linear $f$-expectation (induced by a BSDE) without making any regularity assumptions on the reward process $\xi$. and with general filtration. We show that the value family can be aggregated by an optional process $Y$. We characterize the process $Y$ as the $\mathcal{E}^f$-Snell envelope of $\xi$. We also establish an infinitesimal characterization of the value process $Y$ in terms of a Reflected BSDE with $\xi$ as the obstacle. To do this, we first establish a comparison theorem for irregular RBSDEs. We give an application to the pricing of American options with irregular pay-off in an imperfect market model.

Suggested Citation

  • Miryana Grigorova & Peter Imkeller & Youssef Ouknine & Marie-Claire Quenez, 2020. "Optimal stopping with f -expectations: the irregular case," Post-Print hal-01403616, HAL.
    • Handle: RePEc:hal:journl:hal-01403616
    DOI: 10.1016/j.spa.2019.05.001
    Note: View the original document on HAL open archive server: https://hal.science/hal-01403616v5
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    References listed on IDEAS

    as
    1. Miryana Grigorova & Marie-Claire Quenez, 2017. "Optimal stopping and a non-zero-sum Dynkin game in discrete time with risk measures induced by BSDEs," Papers 1705.03724, arXiv.org.
    2. Miryana Grigorova & Marie-Claire Quenez, 2017. "Optimal stopping and a non-zero-sum Dynkin game in discrete time with risk measures induced by BSDEs," Post-Print hal-01519215, HAL.
    3. Erhan Bayraktar & Song Yao, 2009. "Optimal Stopping for Non-linear Expectations," Papers 0905.3601, arXiv.org, revised Jan 2011.
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    Cited by:

    1. Marzougue, Mohamed, 2023. "Non-linear Dynkin games over split stopping times," Statistics & Probability Letters, Elsevier, vol. 193(C).

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