Optimal stopping with f-expectations: The irregular case
| Autor: | Miryana Grigorova, Youssef Ouknine, Peter Imkeller, Marie-Claire Quenez |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
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 |
| Zdroj: | Stochastic Processes and their Applications. 130:1258-1288 |
| ISSN: | 0304-4149 |
| DOI: | 10.1016/j.spa.2019.05.001 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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