Representation for filtration-consistent nonlinear expectations under a general domination condition

TL;DR

This paper establishes a representation theorem for a broad class of filtration-consistent nonlinear expectations satisfying a general domination condition, linking them to solutions of specific backward stochastic differential equations with particular generator properties.

Contribution

It extends the representation of nonlinear expectations to those dominated by a general class, characterized by generators independent of y and uniformly continuous in z.

Findings

Nonlinear expectations can be represented via BSDEs with specific generator conditions.

The domination condition broadens the class of expectations that can be characterized.

Generators are independent of y and uniformly continuous in z, facilitating the representation.

Abstract

In this paper, we consider filtration-consistent nonlinear expectations which satisfy a general domination condition (dominated by ${\cal{E}}^{\phi}$). We show that this kind of nonlinear expectations can be represented by $g$-expectations defined by the solutions of backward stochastic differential equations, whose generators are independent on $y$ and uniformly continuous in $z$.