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

2006/02/15 by Shanjian Tang, Tang, Shanjian
Economics, Econometrics and Finance · Mathematics · #49L20 #60H10 #60H30 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.OC #math.PR #msc:49L20 #msc:60H10 #msc:60H30

paper · pdf · doi:10.48550/arxiv.math/0602323

8 pages

arxiv created 2006/02/15 · openalex publication_date 2006/02/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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