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18.642

Topics in Mathematics with Applications in Finance

Dr. Peter Kempthorne, Dr. Vasily Strela, Dr. Jake Xia | Fall 2024

Business & Management Finance & Accounting Science & Math Mathematics Applied Mathematics Business Finance Probability and Statistics

前往原始課程

CC BY-NC-SA 4.0

課程簡介

This is an updated version of 18.S096 Topics in Mathematics with Applications in Finance from Fall 2013. Please visit the 18.S096 site for more materials and lecture recordings. An investment game is also available as an additional learning resource.

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.

Course Information

Source	MIT 開放式課程
科系	Mathematics
Language	English
影片數	22

課程影片 (22)

Lecture 1, Part I: Introduction of the Class

Lecture 1, Part I: Introduction of the Class

Lecture 1, Part II: Introduction of Financial Markets, Financial Terms and Concepts

Lecture 1, Part II: Introduction of Financial Markets, Financial Terms and Concepts

Lecture 1, Part III: Bond “Mathematics”

Lecture 1, Part III: Bond “Mathematics”

Lecture 2: Linear Algebra

Lecture 2: Linear Algebra

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

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

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

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

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

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

Lecture 7: Linear Rates, Products, and Models

Lecture 7: Linear Rates, Products, and Models

Lecture 8: Regression Analysis (cont.)

Lecture 8: Regression Analysis (cont.)

Lecture 9: Principal Component Analysis in Finance

Lecture 9: Principal Component Analysis in Finance

Lecture 10: Counterparty Risk Optimization

Lecture 10: Counterparty Risk Optimization

Lecture 11: Regression Analysis (cont.)

Lecture 11: Regression Analysis (cont.)

Lecture 13: Portfolio Management

Lecture 13: Portfolio Management

Lecture 14: Stochastic Processes II

Lecture 14: Stochastic Processes II

Lecture 12: Time Series Analysis

Lecture 12: Time Series Analysis

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

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

Lecture 19: Volatility Modeling

Lecture 19: Volatility Modeling

Lecture 21: Black-Scholes Formula, Risk Neutral Valuation

Lecture 21: Black-Scholes Formula, Risk Neutral Valuation

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

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

Lecture 23: Introduction to Machine Learning

Lecture 23: Introduction to Machine Learning

Lecture 24: Stochastic Calculus

Lecture 24: Stochastic Calculus

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

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