Monte Carlo Methods and Optimization Methods

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

  1. Monte Carlo Methods in Financial Engineering, Paul Glasserman
  2. Practical Optimization: Algorithms and Engineering Applications, Andreas Antoniou, Wu-Sheng Lu
  3. Convex Optimization – Boyd and Vandenberghe
  4. Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, Aharon Ben-Tal, Arkadi Nemirovski