Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control
We study the partial differential equation max{Lu − f, H(Du)} = 0 where is the unknown function, is a second-order elliptic operator, is a given smooth function and 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 Hölder continuous gradient. We also show that if is convex, the gradient of this solution is Lipschitz...