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Viscosity Solutions to Path-Dependent HJB Equation and Applications (1611.05533v4)
Published 17 Nov 2016 in math.OC
Abstract: In this article, the notion of viscosity solution is introduced for the path-dependent Hamilton-Jacobi-BeLLMan (PHJB) equations associated with the optimal control problems for path-dependent stochastic differential equations. We identify the value functional of the optimal control problems as unique viscosity solution to the associated PHJB equations. Applications to backward stochastic Hamilton-Jacobi-BeLLMan equations are also given.