Topics in Mathematics with Applications in Finance

The purpose of the class is to expose undergraduate and graduate students to the mathematical concepts and techniques used in the financial industry. Mathematics lectures are mixed with lectures illustrating the corresponding application in the financial industry. MIT mathematicians teach the mathematics part while industry professionals give the lectures on applications in finance.

1. Introduction, Financial Terms and Concepts.
2. Linear Algebra.
3. Probability Theory.
5. Stochastic Processes I.
6. Regression Analysis.
7. Value At Risk (VAR) Models.
8. Time Series Analysis I.
9. Volatility Modeling.
10. Regularized Pricing and Risk Models.
11. Time Series Analysis II.
12. Time Series Analysis III.
13. Commodity Models.
14. Portfolio Theory.
15. Factor Modeling.
16. Portfolio Management.
17. Stochastic Processes II.
18. Itō Calculus.
19. Black-Scholes Formula, Risk-neutral Valuation.
20. Option Price and Probability Duality.
21. Stochastic Differential Equations.
23. Quanto Credit Hedging.
24. HJM Model for Interest Rates and Credit.
25. Ross Recovery Theorem.
26. Introduction to Counterparty Credit Risk.