On Lenglart's Theory of Meyer-sigma-fields and El Karoui's Theory of Optimal Stopping

2018/10/19 by Bank, Peter, Besslich, David
#60H30 #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.1810.08485

Abstract

We summarize the general results of El Karoui [1981] on optimal stopping problems for processes which are measurable with respect to Meyer-σ-fields. Meyer-σ-fields are due to Lenglart [1980] and include the optional and predictable σ-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 Föllmer [2003].

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