# Optimal stopping with f -expectations: the irregular case

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 $\xi$. 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 :
Type de document :
Pré-publication, Document de travail
2018
Domaine :

Littérature citée [44 références]

https://hal.archives-ouvertes.fr/hal-01403616
Contributeur : Miryana Grigorova <>
Soumis le : lundi 12 février 2018 - 13:04:03
Dernière modification le : mercredi 21 mars 2018 - 18:56:49
Document(s) archivé(s) le : lundi 7 mai 2018 - 02:55:28

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• HAL Id : hal-01403616, version 4
• ARXIV : 1611.09179

### Citation

Miryana Grigorova, Peter Imkeller, Youssef Ouknine, Marie-Claire Quenez. Optimal stopping with f -expectations: the irregular case. 2018. 〈hal-01403616v4〉

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