A numerical method for backward stochastic differential equations with applications in finance.

This thesis starts by discussing the foundations of mathematical finance and some theoretical results on backward stochastic differential equations. We discuss some examples of these equations in mathematical finance (primarily option pricing) and develop a numerical method that can approximate solutions to these equations. Subsequently, we extend the framework to so called reflected backward stochastic differential equations and extend the numerical method to this new type of equation. This enables us to price a wide range of American options. Finally, we discuss a two-dimensional example and extend the numerical method to cope with this problem. This extension enables the pricing of options on two underlyings and we use the numerical method to price a spread option. In the final section we present the conclusions of this research.Applied mathematicsElectrical Engineering, Mathematics and Computer Scienc