Date of Award
May 2017
Degree Type
Thesis
Degree Name
Master of Science
Department
Mathematics
First Advisor
Bruce Wade
Committee Members
Richard Stockbridge, Chao Zhu
Keywords
Hamilton-Jacobi-Bellman, Howard, Monotone Schemes, Numerics, Optimal Control, Viscosity
Abstract
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.
Recommended Citation
Greif, Constantin, "Numerical Methods for Hamilton-Jacobi-Bellman Equations" (2017). Theses and Dissertations. 1480.
https://dc.uwm.edu/etd/1480
Matlab Codes