Random G-expectations

TL;DR

This paper introduces a new probabilistic framework for time-consistent sublinear expectations under stochastic volatility uncertainty, extending Peng's G-expectation to more general, path-dependent settings.

Contribution

It develops a purely probabilistic construction of a stochastic volatility G-expectation using an optimal control approach with path-dependent control sets.

Findings

Extended G-expectation to stochastic volatility scenarios

Provided a probabilistic construction method

Ensured time-consistency in the new framework

Abstract

We construct a time-consistent sublinear expectation in the setting of volatility uncertainty. This mapping extends Peng's G-expectation by allowing the range of the volatility uncertainty to be stochastic. Our construction is purely probabilistic and based on an optimal control formulation with path-dependent control sets.