On Lenglart's Theory of Meyersigmafields and El Karoui's Theory of Optimal Stopping
Abstract
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 Meyerprojections. 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{ö}llmer [2003].
 Publication:

arXiv eprints
 Pub Date:
 October 2018
 arXiv:
 arXiv:1810.08485
 Bibcode:
 2018arXiv181008485B
 Keywords:

 Mathematics  Probability;
 Mathematics  Optimization and Control;
 60H30