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Optimal stopping with f-expectations: The irregular case
- Source :
- Stochastic Processes and their Applications. 130:1258-1288
- Publication Year :
- 2020
- Publisher :
- Elsevier BV, 2020.
-
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.
- 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
Subjects
Details
- ISSN :
- 03044149
- Volume :
- 130
- Database :
- OpenAIRE
- Journal :
- Stochastic Processes and their Applications
- Accession number :
- edsair.doi...........780e62b83d5f31e18f948e640147e861