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2008•SIAM Journal on Control and OptimizationRequires access

Dynamic Programming Principle for One Kind of Stochastic Recursive Optimal Control Problem and Hamilton–Jacobi–Bellman Equation

Zhen Wu, Zhiyong Yu

Open publisher page 67 citations

Abstract

In this paper, we study one kind of stochastic recursive optimal control problem with the obstacle constraint for the cost functional described by the solution of a reflected backward stochastic differential equation. We give the dynamic programming principle for this kind of optimal control problem and show that the value function is the unique viscosity solution of the obstacle problem for the corresponding Hamilton–Jacobi–Bellman equation.

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What this paper is about

In this paper, we study one kind of stochastic recursive optimal control problem with the obstacle constraint for the cost functional described by the solution of a reflected backward stochastic differential equation. We give the dynamic programming principle for this kind of optimal control problem and show that the value function is the unique viscosity solution of the obstacle problem for the corresponding Hamilton–Jacobi–Bellman equation.

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OpenAlex reports 67 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we study one kind of stochastic recursive optimal control problem with the obstacle constraint for the cost functional described by the solution of a reflected backward stochastic differential equation. We give the dynamic programming principle for this kind of optimal control problem and show that the value function is the unique viscosity solution of the obstacle problem for the corresponding Hamilton–Jacobi–Bellman equation.

Key concepts: Bellman equation, Dynamic programming, Viscosity solution, Optimal control, Mathematics, Hamilton–Jacobi equation, Hamilton–Jacobi–Bellman equation, Stochastic control

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