# 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 $\xi$. 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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Cited literature [45 references]

https://hal.archives-ouvertes.fr/hal-01403616
Contributor : Miryana Grigorova <>
Submitted on : Wednesday, August 1, 2018 - 3:13:51 AM
Last modification on : Friday, March 27, 2020 - 4:03:31 AM

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### Identifiers

• HAL Id : hal-01403616, version 5
• ARXIV : 1611.09179

### Citation

Miryana Grigorova, Peter Imkeller, Youssef Ouknine, Marie-Claire Quenez. Optimal stopping with f -expectations: the irregular case. 2018. ⟨hal-01403616v5⟩

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