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Viscosity Solutions to First Order Path-Dependent HJB Equations

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.

preprint2020arXivOpen access
Jianjun Zhou
math.APmath.OC
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Jianjun Zhou

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