The G-convex Functions Based on the Nonlinear Expectations Defined by G-BSDEs

TL;DR

This paper introduces a new class of G-convex functions based on G-Brownian motion-driven backward stochastic differential equations, extending Peng's original G-convex functions within the framework of G-expectations.

Contribution

It generalizes the concept of G-convex functions by defining a new group based on G-BSDEs, expanding the theoretical framework of G-expectations.

Findings

Defined a new class of G-convex functions using G-BSDEs

Extended Peng's G-convex functions to a broader setting

Provided properties and potential applications of the new G-convex functions

Abstract

In this paper, generalizing the definition of G-convex functions defined by Peng [9] during the construction of G-expectations and related properties, we define a group of G-convex functions based on the Backward Stochastic Differential Equations driven by G- Brownian motions.