Viscosity methods, Hamilton-Jacobi-Bellman equations, and applications to finance

Hamilton-jacobi-Bellman equations arise in optimal control theory for stochastic processes. This theory has many important applications, e.g. within finance. An important example is pricing of options. A popular way to solve optimal control problems, has solving the corresponding Hamilton-Jacobi-Bellman equations as the main ingredient. However the solutions to these equations can not be written as explicit closed form expressions, so numerical methods are needed. In this project numerical methods for sol ving such problems will be studied. The goal being to derive the rates of convergence, i.e. the speed of convergence of these methods. Different numerical methods and different Hamilton-Jacobi-Bellman equations will be considered. And, in addition to deve loping new mathematical theory, concrete applications to finance will be studied.