Constructing Sublinear Expectations on Path Space
arXiv:1205.2415 · doi:10.1016/j.spa.2013.03.022
Abstract
We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization of the random G-expectation, and an optional sampling theorem that holds without exceptional set. Our results also shed light on the inherent limitations to constructing sublinear expectations through aggregation.
28 pages; forthcoming in 'Stochastic Processes and their Applications'