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.
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https://hal.archives-ouvertes.fr/hal-01403616
Contributeur : Miryana Grigorova <>
Soumis le : mercredi 19 juillet 2017 - 22:15:57
Dernière modification le : jeudi 27 juillet 2017 - 01:11:39

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  • HAL Id : hal-01403616, version 3
  • ARXIV : 1611.09179

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Miryana Grigorova, Peter Imkeller, Youssef Ouknine, Marie-Claire Quenez. Optimal stopping with f -expectations: the irregular case. 2017. 〈hal-01403616v3〉

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