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

Abstract

In this paper, we consider filtration-consistent nonlinear expectations which satisfy a general domination condition (dominated by ${\mathcal{E}}^{\varphi }$). 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 $z$.

21 pages, Remark 3.1 is rewritten. Assumption (H2) in the results are eliminated. Comments are welcome

References in corpus (1)

• Choquet expectation and Peng's g-expectation