Monte Carlo Methods and Optimization Methods
Archived page from the Certificate in Quantitative Investment (CQI) section of the original site. For current information see en.cqi.sg.
Course Description
Monte Carlo Methods and Optimization Methods…
Course Outline
| Session | Topics | Readings | Homeworks |
| 1 | Generate random numbers | Lecturer handout | hw1 |
| 2 | Generate random processes | Lecturer handout | hw2 |
| 3 | Variance reduction techniques | Lecturer handout | hw3 |
| 4 | Quasi-Monte Carlo | Lecturer handout | hw4 |
| 5 | Discretization methods | Lecturer handout | hw5 |
| 6 | Estimating sensitivities | Lecturer handout | hw6 |
| 7 | Sequential importance sampling and resampling | Lecturer handout | hw7 |
| 8 | Linear programming | Lecturer handout | hw8 |
| 9 | Quadratic programming | Lecturer handout | hw9 |
| 10 | Second-order conic programming | Lecturer handout | hw10 |
| 11 | Mixed-Integer (non-)linear programming | Lecturer handout | hw11 |
| 12 | (Stochastic) linear quadratic regulator problems | Lecturer handout | hw12 |
Recommended Readings
- Monte Carlo Methods in Financial Engineering, Paul Glasserman
- Practical Optimization: Algorithms and Engineering Applications, Andreas Antoniou, Wu-Sheng Lu
- Convex Optimization – Boyd and Vandenberghe
- Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, Aharon Ben-Tal, Arkadi Nemirovski