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Mathematics
Mathematical Finance
1. Foundations of Mathematical Finance
2. Probability Theory for Finance
3. Discrete-Time Financial Models
4. Stochastic Calculus
5. Continuous-Time Models and Derivative Pricing
6. Interest Rate Modeling
7. Advanced Derivative Pricing
8. Credit Risk Modeling
9. Portfolio Theory and Optimization
10. Risk Management
11. Numerical Methods in Finance
10.
Risk Management
10.1.
Market Risk Measurement
10.1.1.
Value at Risk
10.1.1.1.
Parametric Methods
10.1.1.1.1.
Variance-Covariance Approach
10.1.1.1.2.
Delta-Normal Method
10.1.1.2.
Historical Simulation
10.1.1.2.1.
Full Revaluation
10.1.1.2.2.
Weighted Historical Simulation
10.1.1.3.
Monte Carlo Simulation
10.1.1.3.1.
Scenario Generation
10.1.1.3.2.
Model-Based Simulation
10.1.2.
Expected Shortfall
10.1.2.1.
Definition and Properties
10.1.2.2.
Calculation Methods
10.1.2.3.
Coherent Risk Measures
10.1.3.
Stress Testing
10.1.3.1.
Scenario Design
10.1.3.2.
Sensitivity Analysis
10.1.3.3.
Reverse Stress Testing
10.2.
Credit Risk Management
10.2.1.
Credit Exposure Measurement
10.2.1.1.
Current Exposure
10.2.1.2.
Potential Future Exposure
10.2.1.3.
Expected Exposure
10.2.2.
Credit Risk Mitigation
10.2.2.1.
Netting Agreements
10.2.2.2.
Collateral Management
10.2.2.3.
Credit Derivatives
10.2.3.
Credit Valuation Adjustments
10.2.3.1.
CVA Calculation
10.2.3.2.
DVA Calculation
10.2.3.3.
FVA and Other XVAs
10.3.
Operational Risk
10.3.1.
Operational Risk Framework
10.3.2.
Loss Distribution Approach
10.3.3.
Scenario Analysis
10.3.4.
Key Risk Indicators
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11. Numerical Methods in Finance