1 Introduction

2 Monte Carlo Simulation
  2.1 Random number generation
  2.2 Monte Carlo method
  2.3 Quasi Monte Carlo simulation
  2.4 Pricing American options with Monte Carlo

3 Discretization of stochastic partial differential equations
  3.1 Generating sample paths
  3.2 The Euler method
  3.3 Advanced method

4 Stochastic differential equations
4.1 The finite difference method
4.2 Fourier method

Appendix
1. Existence and Uniqueness
2. The Freyman Karc formula
3. The first variation
4. Hormander’s theorem