Date of Award
Master of Science
Richard Stockbridge, Chao Zhu
Hamilton-Jacobi-Bellman, Howard, Monotone Schemes, Numerics, Optimal Control, Viscosity
In this work we considered HJB equations, that arise from stochastic optimal control problems
with a finite time interval. If the diffusion is allowed to become degenerate, the solution cannot be
understood in the classical sense. Therefore one needs the notion of viscosity solutions. With some
stability and consistency assumptions, monotone methods provide the convergence to the viscosity
solution. In this thesis we looked at monotone finite difference methods, semi lagragian methods and
finite element methods for isotropic diffusion. In the last chapter we introduce the vanishing moment
method, a method not based on monotonicity.
Greif, Constantin, "Numerical Methods for Hamilton-Jacobi-Bellman Equations" (2017). Theses and Dissertations. 1480.