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18.642 | Fall 2024 | Undergraduate

# Topics in Mathematics with Applications in Finance

The course consists of a mix of mathematics lectures taught by MIT instructors and lectures on applications in finance given by industry professionals.

Lecture 1: Introduction. Financial Terms and Concepts. Bond Math.

Peter Kempthorne, Jake Xia, Vasily Strela

Lecture 2: Linear Algebra

Math Lecture: Peter Kempthorne

Lecture 3: Quantitative Equity Investing

Applications Lecture: Jeff Shen, BlackRock Investment Institute

Problem Set 1 due

Lecture 4: Linear Algebra (cont.); Probability Theory

Math Lecture: Peter Kempthorne

Lecture 5: Probability Theory (cont.); Stochastic Processes I

Math Lecture: Peter Kempthorne

Lecture 6: Stochastic Processes I (cont.); Regression Analysis

Math Lecture: Peter Kempthorne

Lecture 7: Linear Rates, Products, and Models

Applications Lecture: Andrew Gunstensen, Mizuho Financial Group

Problem Set 2 due

Lecture 8: Regression Analysis (cont.)

Math Lecture: Peter Kempthorne

Lecture 9: Principal Component Analysis in Finance

Applications Lecture: Stefan Andreev, Two Sigma Investments

Problem Set 3 due

Lecture 10: Counterparty Risk Optimization

Applications Lecture: James Shepherd, Quantile Technologies (LSEG)

Lecture 11: Regression Analysis (cont.)

Math Lecture: Peter Kempthorne

Lecture 12: Time Series Analysis

Math Lecture: Peter Kempthorne

Lecture 13: Portfolio Management

Applications Lecture: Jake Xia

Lecture 14: Stochastic Processes II

Math Lecture: Peter Kempthorne

Lecture 15

Student Presentations of Mid-Semester Group Project

Lecture 16

Student Presentations of Mid-Semester Group Project

Lecture 17

Student Presentations of Mid-Semester Group Project

Lecture 18: Applying Data Science and Artificial Intelligence to Managing Biomedical Portfolios

Applications Lecture: Andrew W. Lo, MIT Sloan School of Management

Problem Set 4 due

Lecture 19: Volatility Modeling

Math Lecture: Peter Kempthorne

Lecture 20: Building the First Federally (CFTC) Regulated Exchange Dedicated to Trading on Events

Applications Lecture: Tarek Mansour, Kalshi.com Financial Exchange and Prediction Market

Lecture 21: Black-Scholes Formula, Risk Neutral Valuation

Applications Lecture: Vasily Strela

Lecture 22: The Spectrum of Systematic Trading Strategies in Liquid Instruments

Applications Lecture: Ross Garon, Millennium Management

Problem Set 5 due

Lecture 23: Introduction to Machine Learning

Applications Lecture: John Hull, University of Toronto

Lecture 24: Stochastic Calculus

Math Lecture: Peter Kempthorne

Lecture 25: Stochastic Calculus (cont.); Stochastic Differential Equations

Math Lecture: Peter Kempthorne

Lecture 26

Final Paper Student Presentations

## Course Info

##### Instructors

- Dr. Peter Kempthorne
- Dr. Vasily Strela
- Dr. Jake Xia

##### Departments

- Mathematics

##### As Taught In

Fall 2024

##### Level

Undergraduate

##### Topics

- Business
  - Finance
- Mathematics
  - Applied Mathematics
  - Probability and Statistics

##### Learning Resource Types

notes Lecture Notes
theaters Lecture Videos
assignment Problem Sets
assignment Activity Assignments
group_work Projects
Readings

Browse Resources

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