Constructing Sublinear Expectations on Path Space

TL;DR

This paper develops a general framework for constructing time-consistent sublinear expectations on path space, extending G-expectation theory and addressing aggregation limitations.

Contribution

It introduces a new method for constructing sublinear expectations on continuous paths, including a generalized conditional G-expectation and an optional sampling theorem without exceptional sets.

Findings

Existence of conditional G-expectation for Borel-measurable variables

Generalization of random G-expectation

An optional sampling theorem without exceptional sets

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.