Sublinear Expectations and Martingales in discrete time

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.

References in corpus (4)

• Martingale Representation Theorem for the G-expectation
• A general theory of Finite State Backward Stochastic Difference Equations
• Dynamically Consistent Nonlinear Evaluations and Expectations
• Weak Approximation of G-Expectations

Cited by in corpus (10)

• Optimal Stopping under Model Ambiguity: a Time-Consistent Equilibrium Approach
• A monotone scheme for G-equations with application to the explicit convergence rate of robust central limit theorem
• Coherent Price Systems and Uncertainty-Neutral Valuation
• Some inequalities and limit theorems under sublinear expectations
• Partial Uncertainty and Applications to Risk-Averse Valuation
• Backward stochastic differential equations with regime-switching and sublinear expectations
• Quasi-sure analysis, aggregation and dual representations of sublinear expectations in general spaces
• Convergence rates in the law of large numbers under sublinear expectations
• A Note on $G$- Optimal Stopping Problems
• Doob's optional sampling and maximal inequality for $G$-martingales