On the representation for dynamically consistent nonlinear evaluations: uniformly continuous case

Abstract

A system of dynamically consistent nonlinear evaluation ($\mathcal{F}$-evaluation) provides an ideal characterization for the dynamical behaviors of risk measures and the pricing of contingent claims. The purpose of this paper is to study the representation for the $\mathcal{F}$-evaluation by the solution of a backward stochastic differential equation (BSDE). Under a general domination condition, we prove that any $\mathcal{F}$-evaluation can be represented by the solution of a BSDE with a generator which is Lipschitz in $y$ and uniformly continuous in $z$.

34 pages. minor corrections. Comments are welcome

References in corpus (2)

• Dynamically Consistent Nonlinear Evaluations and Expectations
• Representation for filtration-consistent nonlinear expectations under a general domination condition