Non-stopping times and stopping theorems
Copyright policy )Non-stopping times and stopping theorems
Given a random time, we characterize the set of martingales for which the stopping theorems still hold. We also investigate how the stopping theorems are modified when we consider arbitrary random times. To this end, we introduce some families of martingales with remarkable properties. We also investigate, in the Brownian setting, the relationships between a given random time and the underlying Brownian Motion in the progressively enlarged filtration with respect to this random time.
Typos corrected. Close to the published version
- ETH Zurich Switzerland
- University of Zurich Switzerland
Statistics and Probability, Stopping times; optimal stopping problems; gambling theory, 05C38, 15A15, 15A18, Martingales with continuous parameter, random times, Martingales, optional stopping theorem, Random times, 510 Mathematics, 2604 Applied Mathematics, martingales, Modelling and Simulation, FOS: Mathematics, Optional stopping theorem, 2613 Statistics and Probability, Zeros of continuous martingales, Applied Mathematics, Probability (math.PR), zeros of continuous martingales, 10123 Institute of Mathematics, Progressive enlargement of filtrations, progressive enlargement of filtrations, Mathematics - Probability, 2611 Modeling and Simulation
Statistics and Probability, Stopping times; optimal stopping problems; gambling theory, 05C38, 15A15, 15A18, Martingales with continuous parameter, random times, Martingales, optional stopping theorem, Random times, 510 Mathematics, 2604 Applied Mathematics, martingales, Modelling and Simulation, FOS: Mathematics, Optional stopping theorem, 2613 Statistics and Probability, Zeros of continuous martingales, Applied Mathematics, Probability (math.PR), zeros of continuous martingales, 10123 Institute of Mathematics, Progressive enlargement of filtrations, progressive enlargement of filtrations, Mathematics - Probability, 2611 Modeling and Simulation
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