Topics in Mathematics with Applications in Finance

This is an updated version of {{% resource_link "27e63b7c-484a-4e85-bf49-460d6c108ea2" "*18.S096 Topics in Mathematics with Applications in Finance*" %}} from Fall 2013. Please visit the {{% resource_link "27e63b7c-484a-4e85-bf49-460d6c108ea2" "*18.S096* site" %}} for more materials and lecture recordings. We are planning to add a trading game as an additional learning resource. The link will be published on this page. Stay tuned! The purpose of the class is to expose undergraduate and graduate students to the mathematical concepts and techniques used in the financial industry. The course will consist of a set of mathematics lectures on topics in linear algebra, probability, statistics, stochastic processes, and numerical methods. Mathematics lectures will be mixed with lectures illustrating the corresponding application in the financial industry. MIT mathematicians will teach the mathematics part while industry professionals will give the lectures on applications in finance.

Syllabus

Lecture 1, Part I: Introduction of the Class
Lecture 1, Part II: Introduction of Financial Markets, Financial Terms and Concepts
Lecture 1, Part III: Bond “Mathematics”
Lecture 2: Linear Algebra
Lecture 4: Linear Algebra (cont.); Probability Theory
Lecture 5: Probability Theory (cont.); Stochastic Processes I
Lecture 6: Stochastic Processes I (cont.); Regression Analysis
Lecture 7: Linear Rates, Products, and Models
Lecture 8: Regression Analysis (cont.)
Lecture 9: Principal Component Analysis in Finance
Lecture 10: Counterparty Risk Optimization
Lecture 11: Regression Analysis (cont.)
Lecture 12: Time Series Analysis
Lecture 13: Portfolio Management
Lecture 14: Stochastic Processes II
Lecture 19: Volatility Modeling
Lecture 20: Building the First Federally (CFTC) Regulated Exchange Dedicated to Trading on Events
Lecture 21: Black-Scholes Formula, Risk Neutral Valuation
Lecture 23: Introduction to Machine Learning
Lecture 24: Stochastic Calculus
Lecture 25: Stochastic Calculus (cont.); Stochastic Differential Equations