Optimal stopping with f -expectations: the irregular case

Miryana Grigorova (), Peter Imkeller, Youssef Ouknine and Marie-Claire Quenez ()
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Miryana Grigorova: Universität Bielefeld = Bielefeld University
Peter Imkeller: Institut für Mathematik [Berlin] - TUB - 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

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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.

Keywords: optimal stopping; backward stochastic differential equation; f-expectation; nonlinear expectation; aggregation; American option; dynamic risk measure; strong $\mathcal{E}^f$ -supermartingale; Snell envelope; reflected backward stochastic differential equation; comparison theorem; Tanaka-type formula; General filtration (search for similar items in EconPapers)
Date: 2020
Note: View the original document on HAL open archive server: https://hal.science/hal-01403616v5
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Citations: View citations in EconPapers (1)

Published in Stochastic Processes and their Applications, 2020, 130 (3), pp.1258--1288. ⟨10.1016/j.spa.2019.05.001⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01403616

DOI: 10.1016/j.spa.2019.05.001

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