Viscosity Solutions to Path-Dependent HJB Equation and Applications

2016/11/17 by Zhou, Jianjun
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1611.05533

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.

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