On Lenglart's Theory of Meyer-sigma-fields and El Karoui's Theory of Optimal Stopping
| Autor: | Bank, Peter, Besslich, David |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | We summarize the general results of El Karoui [1981] on optimal stopping problems for processes which are measurable with respect to Meyer-$\sigma$-fields. Meyer-$\sigma$-fields are due to Lenglart [1980] and include the optional and predictable $\sigma$-field as special cases. Novel contributions of our work are path regularity results for Meyer measurable processes and limit results for Meyer-projections. We will also clarify a minor issue in the proof of the optimality result in El Karoui [1981]. These extensions were inspired and needed for the proof of a stochastic representation theorem in Bank and Besslich [2018a]. As an application of this theorem, we provide an alternative approach to optimal stopping in the spirit of Bank and F{\"o}llmer [2003]. |
| Databáze: | arXiv |
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