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

2012/07/05 by Shaolin Ji, Ji, Shaolin, Shuzhen Yang +1
Economics, Econometrics and Finance · Mathematics · Social Sciences · #Economic theories and models #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications #math.OC #math.PR

paper · pdf · doi:10.48550/arxiv.1207.1194

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openalex publication_date 2012/07/05 · arxiv created 2013/01/01 · arxiv updated 2013/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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