Optimal stopping with f -expectations: the irregular case

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

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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.

Date: 2016-11, Revised 2018-08
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1611.09179

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