Dual Representation as Stochastic Differential Games of Backward Stochastic Differential Equations and Dynamic Evaluations

Shanjian Tang

Published 2006-02-15Version 1

In this Note, assuming that the generator is uniform Lipschitz in the unknown variables, we relate the solution of a one dimensional backward stochastic differential equation with the value process of a stochastic differential game. Under a domination condition, a filtration-consistent evaluations is also related to a stochastic differential game. This relation comes out of a min-max representation for uniform Lipschitz functions as affine functions. The extension to reflected backward stochastic differential equations is also included.