Sublinear Expectations and Martingales in discrete time

TL;DR

This paper develops a theory of sublinear expectations and martingales in discrete time without relying on a dominating probability measure, extending classical results and including a theory of BSDEs in finite-state spaces.

Contribution

It introduces a novel framework for sublinear expectations and martingales in discrete time, generalizing classical probabilistic results without a dominating measure.

Findings

Extended classical martingale results to sublinear expectation setting

Developed a theory of BSDEs in finite-state spaces under sublinear expectations

Proved existence and comparison theorems for BSDEs in this context

Abstract

We give a theory of sublinear expectations and martingales in discrete time. Without assuming the existence of a dominating probability measure, we derive the extensions of classical results on uniform integrability, optional stopping of martingales, and martingale convergence. We also give a theory of BSDEs in the context of sublinear expectations and a finite-state space, including general existence and comparison results.