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Article Dans Une Revue Stochastic Processes and their Applications Année : 2020

Optimal stopping with f -expectations: the irregular case

Résumé

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.
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Dates et versions

hal-01403616 , version 1 (26-11-2016)
hal-01403616 , version 2 (27-05-2017)
hal-01403616 , version 3 (19-07-2017)
hal-01403616 , version 4 (12-02-2018)
hal-01403616 , version 5 (01-08-2018)

Identifiants

Citer

Miryana Grigorova, Peter Imkeller, Youssef Ouknine, Marie-Claire Quenez. Optimal stopping with f -expectations: the irregular case. Stochastic Processes and their Applications, 2020, 130 (3), pp.1258--1288. ⟨10.1016/j.spa.2019.05.001⟩. ⟨hal-01403616v5⟩
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