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Viscosity Solutions to First Order Path-Dependent HJB Equations (2004.02095v2)
Published 5 Apr 2020 in math.AP and math.OC
Abstract: In this article, a notion of viscosity solutions is introduced for first order path-dependent Hamilton-Jacobi-BeLLMan (HJB) equations associated with optimal control problems for path-dependent differential equations. We identify the value functional of the optimal control problems as a unique viscosity solution to the associated HJB equations. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property.