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

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

2006-02-15

arxiv.org/abs/math/0602323v1

Mathematics

Probability

8 pages

Scientific paper

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.

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