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Optimal Stopping With ƒ-Expectations: the irregular case

Author

Listed:
  • Grigorova, Miryana

    (Center for Mathematical Economics, Bielefeld University)

  • Imkeller, Peter

    (Center for Mathematical Economics, Bielefeld University)

  • Ouknine, Youssef

    (Center for Mathematical Economics, Bielefeld University)

  • Quenez, Marie-Claire

    (Center for Mathematical Economics, Bielefeld University)

Abstract

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

Suggested Citation

  • Grigorova, Miryana & Imkeller, Peter & Ouknine, Youssef & Quenez, Marie-Claire, 2018. "Optimal Stopping With ƒ-Expectations: the irregular case," Center for Mathematical Economics Working Papers 587, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:587
    as

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    File URL: https://pub.uni-bielefeld.de/download/2930423/2930450
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    References listed on IDEAS

    as
    1. Bayraktar, Erhan & Yao, Song, 2011. "Optimal stopping for non-linear expectations--Part I," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 185-211, February.
    2. Erhan Bayraktar & Ioannis Karatzas & Song Yao, 2009. "Optimal Stopping for Dynamic Convex Risk Measures," Papers 0909.4948, arXiv.org, revised Nov 2009.
    3. 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.
    4. Erhan Bayraktar & Song Yao, 2009. "Optimal Stopping for Non-linear Expectations," Papers 0905.3601, arXiv.org, revised Jan 2011.
    5. Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.
    6. Quenez, Marie-Claire & Sulem, Agnès, 2013. "BSDEs with jumps, optimization and applications to dynamic risk measures," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3328-3357.
    Full references (including those not matched with items on IDEAS)

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