Optimal stopping with f-expectations: The irregular case

By Miryana Grigorova, Peter Imkeller, Y. Ouknine, Marie Claire Quenez. Stochastic Processes and their Applications, 2016

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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.

Subfields: Finance, Management Information Systems, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/12a4fbeffe46a2510eb4683bed5d2b1072d3e715