Quantitative Methods

  1. Computational Methods and Simulation
    1. Monte Carlo Methods
      1. Principles of Monte Carlo Simulation
        1. Random Sampling
          1. Law of Large Numbers
            1. Central Limit Theorem Applications
            2. Random Number Generation
              1. Pseudorandom Numbers
                1. Random Number Generators
                  1. Testing Randomness
                  2. Simulation of Random Variables
                    1. Inverse Transform Method
                      1. Acceptance-Rejection Method
                        1. Box-Muller Transform
                        2. Monte Carlo Integration
                          1. Basic Principles
                            1. Variance Reduction Techniques
                              1. Importance Sampling
                                1. Control Variates
                                  1. Antithetic Variables
                                2. Applications
                                  1. Risk Analysis
                                    1. Portfolio Optimization
                                      1. Option Pricing
                                        1. Reliability Analysis
                                      2. Resampling Methods
                                        1. Bootstrap Methods
                                          1. Non-parametric Bootstrap
                                            1. Parametric Bootstrap
                                              1. Bootstrap Confidence Intervals
                                                1. Percentile Method
                                                  1. Bias-Corrected Method
                                                    1. BCa Method
                                                    2. Bootstrap Hypothesis Testing
                                                    3. Jackknife Methods
                                                      1. Leave-one-out Jackknife
                                                        1. Delete-d Jackknife
                                                          1. Bias Estimation
                                                          2. Permutation Tests
                                                            1. Principles
                                                              1. Exact Tests
                                                                1. Approximate Tests
                                                                2. Cross-Validation
                                                                  1. K-fold Cross-Validation
                                                                    1. Leave-one-out Cross-Validation
                                                                      1. Stratified Cross-Validation
                                                                        1. Time Series Cross-Validation
                                                                      2. Optimization Methods
                                                                        1. Linear Programming
                                                                          1. Problem Formulation
                                                                            1. Graphical Method
                                                                              1. Simplex Method
                                                                                1. Sensitivity Analysis
                                                                                2. Non-linear Optimization
                                                                                  1. Unconstrained Optimization
                                                                                    1. Constrained Optimization
                                                                                      1. Gradient-based Methods
                                                                                        1. Derivative-free Methods
                                                                                        2. Metaheuristic Algorithms
                                                                                          1. Genetic Algorithms
                                                                                            1. Simulated Annealing
                                                                                              1. Particle Swarm Optimization

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                                                                                          4. Advanced Statistical Methods

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                                                                                          6. Introduction to Machine Learning