Mathematical Finance

  1. Risk Management
    1. Market Risk Measurement
      1. Value at Risk
        1. Parametric Methods
          1. Variance-Covariance Approach
            1. Delta-Normal Method
            2. Historical Simulation
              1. Full Revaluation
                1. Weighted Historical Simulation
                2. Monte Carlo Simulation
                  1. Scenario Generation
                    1. Model-Based Simulation
                  2. Expected Shortfall
                    1. Definition and Properties
                      1. Calculation Methods
                        1. Coherent Risk Measures
                        2. Stress Testing
                          1. Scenario Design
                            1. Sensitivity Analysis
                              1. Reverse Stress Testing
                            2. Credit Risk Management
                              1. Credit Exposure Measurement
                                1. Current Exposure
                                  1. Potential Future Exposure
                                    1. Expected Exposure
                                    2. Credit Risk Mitigation
                                      1. Netting Agreements
                                        1. Collateral Management
                                          1. Credit Derivatives
                                          2. Credit Valuation Adjustments
                                            1. CVA Calculation
                                              1. DVA Calculation
                                                1. FVA and Other XVAs
                                              2. Operational Risk
                                                1. Operational Risk Framework
                                                  1. Loss Distribution Approach
                                                    1. Scenario Analysis
                                                      1. Key Risk Indicators

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                                                    9. Portfolio Theory and Optimization

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                                                    11. Numerical Methods in Finance