Date of Award

May 2017

Degree Type


Degree Name

Master of Science



First Advisor

Bruce Wade

Committee Members

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. (2622 kB)
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