1. Optimal stopping with f-expectations: The irregular case
- Author
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Miryana Grigorova, Youssef Ouknine, Peter Imkeller, and Marie-Claire Quenez
- Subjects
Statistics and Probability ,Comparison theorem ,Applied Mathematics ,Infinitesimal ,010102 general mathematics ,Optional stopping theorem ,01 natural sciences ,Dynamic risk measure ,010104 statistics & probability ,Modeling and Simulation ,Snell envelope ,Filtration (mathematics) ,Applied mathematics ,Optimal stopping ,0101 mathematics ,Nonlinear expectation ,Mathematical economics ,Mathematics - 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.
- Published
- 2020