Dr Samuel Cohen (Oxford) - "Conditional expectations under uncertainty"

Abstract

When we consider stochastic processes, we usually fix a probability space, which is complete under a given measure. This guarantees that statements made 'with probability one' or 'almost everywhere' are measurable. When we work with processes under uncertainty, that is, when the probability space is not fixed, things become more complicated. In this talk I will outline the key theoretical difficulties associated with uncertainty, the theory of nonlinear expectations, and some new results allowing us to extend classical results into these pathological settings.