A Viscosity Approach to a Stochastic Control Problem on a Bounded Domain

2009/11/05 by Gong, Ruoting, Houdré, Christian
#35D40 #35K61 #35K65 #49L20 #49L25 #60H10 #60H30 #91G80 #93E20 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0911.0956

Abstract

We study a stochastic control problem on a bounded domain, which arises from a continuous-time optimal management model. Via the corresponding Hamilton-Jacobi-Bellman equation the value function is shown to be jointly continuous and to satisfy the Dynamic Programming Principle. These properties directly lead to the conclusion that the value function is a viscosity solution to the Hamilton-Jacobi-Bellman equation. Uniqueness of the solution is then also established.

Related

• The existence and uniqueness of viscosity solution to a kind of Hamilton-Jacobi-Bellman equations
• Viscosity Solutions of Stochastic Hamilton-Jacobi-Bellman Equations
• Bellman equation and viscosity solutions for mean-field stochastic control problem
• Dynamic Programming Principle and Associated Hamilton-Jacobi-Bellman Equation for Stochastic Recursive Control Problem with Non-Lipschitz Aggregator
• Stochastic optimal control problems with delays in the state and in the control via viscosity solutions and applications to optimal advertising and optimal investment problems