# 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 pay-off 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. This characterization is established by first showing existence and uniqueness for the Reflected BSDE with irregular obstacle and also a comparison theorem.
Keywords :
Type de document :
Pré-publication, Document de travail
2016
Domaine :

https://hal.archives-ouvertes.fr/hal-01403616
Contributeur : Miryana Grigorova <>
Soumis le : samedi 26 novembre 2016 - 20:03:01
Dernière modification le : jeudi 27 avril 2017 - 09:46:11
Document(s) archivé(s) le : mardi 21 mars 2017 - 07:00:08

### Fichiers

Optimal_stopping_with_g-expect...
Fichiers produits par l'(les) auteur(s)

### Identifiants

• HAL Id : hal-01403616, version 1
• ARXIV : 1611.09179

### Citation

Miryana Grigorova, Peter Imkeller, Youssef Ouknine, Marie-Claire Quenez. Optimal stopping with f -expectations: the irregular case. 2016. <hal-01403616>

Consultations de
la notice

## 147

Téléchargements du document