Optimal stopping with f-expectations: The irregular case

Miryana Grigorova, Peter Imkeller, Youssef Ouknine and Marie-Claire Quenez

Stochastic Processes and their Applications, 2020, vol. 130, issue 3, 1258-1288

Abstract: We consider the optimal stopping problem with non-linear f-expectation (induced by a BSDE) without making any regularity assumptions on the payoff process ξ and in the case of a general filtration. We show that the value family can be aggregated by an optional process Y. We characterize the process Y as the Ef-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 some useful properties of irregular RBSDEs, in particular an existence and uniqueness result and a comparison theorem.

Keywords: Reflected backward stochastic differential equation; Non-linear optimal stopping; Ef-Mertens decomposition; General filtration; American option; Tanaka-type formula (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:3:p:1258-1288

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DOI: 10.1016/j.spa.2019.05.001

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