ANALYSIS OF HAMILTON-JACOBI-BELLMAN EQUATIONS ARISING IN STOCHASTIC SINGULAR CONTROL

作者：Hynd Ryan^*

来源：ESAIM: Control, Optimisation and Calculus of Variations , 2013, 19(1): 112-128.

DOI：10.1051/cocv/2012001

• HJB equation
• gradient constraint
• free boundary problem
• singular control
• penalty method
• viscosity solutions

We study the partial differential equation
max {Lu - f, H(Du)} = 0
where u is the unknown function, L is a second-order elliptic operator, f is a given smooth function and H is a convex function. This is a model equation for Hamilton-Jacobi-Bellman equations arising in stochastic singular control. We establish the existence of a unique viscosity solution of the Dirichlet problem that has a Holder continuous gradient. We also show that if H is uniformly convex, the gradient of this solution is Lipschitz continuous.

• 出版日期2013-1