Topics in Mathematics with Applications in Finance (MIT 18.642) - Video lectures 2024
Peter Kempthorne and Vasily Strela and Jake Xia

@article{,
title= {Topics in Mathematics with Applications in Finance (MIT 18.642) - Video lectures 2024},
journal= {},
author= {Peter Kempthorne and Vasily Strela and Jake Xia},
year= {2024},
url= {https://ocw.mit.edu/courses/18-642-topics-in-mathematics-with-applications-in-finance-fall-2024/},
abstract= {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. The schedule includes lecturers from investment banks, FinTech and hedge fund industries as well as academia.

Broad familiarity with linear algebra, statistics, stochastic processes and partial differential equations will be helpful (but not required). Prior knowledge of economics or finance is not required but may be helpful for some lectures.

**Main course URL:** https://ocw.mit.edu/courses/18-642-topics-in-mathematics-with-applications-in-finance-fall-2024/

**Contents:**

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

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**About the Instructors:**

Dr. Peter Kempthorne is a lecturer in the MIT Department of Mathematics on financial mathematics and statistics. He is also president of Kempthorne Analytics and formerly was an associate professor and principal research scientist at MIT Sloan School of Management with research focus on statistical modeling in finance.

Dr. Vasily Strela is a managing director and the global head of fixed income quantitative analytics at RBC Capital Markets. He is also a research affiliate in the MIT Department of Mathematics.

Dr. Jake Xia is a research affiliate in the MIT Department of Mathematics. He is managing director of Harvard Management Company. Prior to that, he was managing director of Morgan Stanley.

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}