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arXiv · 1207.1194

Path-dependent Hamilton-Jacobi-Bellman equations related to controlled stochastic functional differential systems

Shaolin Ji·Shuzhen Yang
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Abstract

In this paper, a stochastic optimal control problem is investigated in which the system is governed by a stochastic functional differential equation. In the framework of functional Itô calculus, we build the dynamic programming principle and the related Path-dependent Hamilton-Jacobi-Bellman (HJB) equation. We prove that the value function is the viscosity solution of the Path-dependent HJB equation.

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Shaolin Ji, Shuzhen Yang. 2013-01-01. Path-dependent Hamilton-Jacobi-Bellman equations related to controlled stochastic functional differential systems. https://arxiv.org/abs/1207.1194

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