Lecture 2: Linear Algebra // TRAIN BRAIN

Lecture 2: Linear Algebra

MIT 18.642 Topics in Mathematics with Applications in Finance, Fall 2024
Instructor: Peter Kempthorne
View the complete course: https://ocw.mit.edu/courses/18-642-topics-in-mathematics-with-applications-in-finance-fall-2024
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP601Q2jo-J_3raNCMMs6Jves
The lecture introduces linear algebra with a focus on its applications in quantitative finance, covering vector and matrix fundamentals, portfolio valuation, and concepts like short selling, arbitrage, and contingent claims. It further explores stochastic matrices and Markov chains, eigenvalues and eigenvectors, and their roles in modeling financial markets, culminating in discussions on no-arbitrage conditions, market completeness, and pricing measures essential for option pricing theory.
License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu
Support OCW at http://ow.ly/a1If50zVRlQ
We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.

MIT OpenCourseWare

A free and open online publication of educational material from thousands of MIT courses, covering the entire MIT curriculum, ranging from introductory to the most advanced graduate courses. On the OCW website, each course includes a syllabus, instruction...

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

Lecture 1, Part III: Bond “Mathematics”

Lecture 13: Portfolio Management

Lecture 14: Stochastic Processes II

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

Lecture 23: Introduction to Machine Learning

Lecture 1, Part I: Introduction of the Class

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

Lecture 21: Black-Scholes Formula, Risk Neutral Valuation

Lecture 2: Linear Algebra

Lecture 8: Regression Analysis (cont.)

Lecture 24: Stochastic Calculus

Lecture 9: Principal Component Analysis in Finance

Lecture 7: Linear Rates, Products, and Models

Lecture 10: Counterparty Risk Optimization

How to Sell Concert Tickets, with MIT Economist Jon Gruber

Can AI fix the economy?

Lecture 11: Contagious Structure in Projection Theory

Lecture 02: Fundamental Methods of Projection Theory

Lecture 13: The Balog-Szemeredi-Gowers Theorem

Lecture 04: The Fourier Method in Euclidean Space

Lecture 09: Reflections on the Szemeredi-Trotter Theorem

Lecture 22: Sharp Projection Theorems, Part 1: Introduction and Beck's Theorem.

Lecture 01: Introduction to Projection Theory

Lecture 23: Sharp Projection Theorems, Part 2: AD Regular Case

Lecture 15: The Bourgain Projection Theorem, Part 2

Lecture 03: Projection Theory in Euclidean Space

Lecture 05: The Large Sieve

Lecture 07: Applications of the Large Sieve to Number Theory

Lecture 20: Homogeneous Dynamics, Part 1

Lecture 10: Sum-Product Theory

Lecture 19: Random Walks on Finite Groups, Part 3

Student Project 2: Ink and Thread: Incorporating Chinese Calligraphy in Fashion

Session 4-1: Networked Geothermal: The European Experience

Session 8-3: Thermal Energy Network Evolution of the Penn South Community in Manhattan

Session 1-3: Health Impacts of Methane ("Natural") Gas Systems

Session 7-3: Techno-Economic Modeling of GENs with HEATNETS Model

Session 5-3: Introduction to Design of GENs

Session 8-2: Framingham, Massachusetts UTEN Pilot Project Overview

Session 6-2: Emerging Code & Standards for Ambient Temperature Loops

Session 5-2: Differences Between Geothermal Heat Pumps and GEN

Session 3-4: Geothermal Energy Networks: Transforming Our Thermal

Session 4-2: Deploying Geothermal Networks At City and Country Scale: Utility Perspective on Scaling

Session 1-2: Carbon Reduction Pathways for Building Stocks

Session 8-1: ATL District Systems Overview

8-4: Intro to the MIT Thermal Energy Networks Plan for Rapid, Cost-Effective Campus Decarbonization

Session 2-1: An Ecological View of the Energy Transition

Session Introduction: Geothermal Energy Networks: Transforming Our Thermal Energy System

Class 15 Video: Encoding Corpora and Voice Leading

Video 7b: Streams as Hierarchies: Types of Containers in music21

Video 6b: Representations of Ontologies: Craig Sapp’s Rosetta Stone

Video 22b: Problem Sets 7-8: Working and Composing with Scales, Chords, and Roman Numerals

Video 7a: Unlocking Duration and Note Objects in music21

Video 12d: How to Work with Ties in music21

Video 6a: Music Representation (III): Unlocking Pitch in music21

Class 27 Video: Feature Extraction and Machine Learning

Video 4b: Music Representation in General

Video 7d: Partwise vs. Timewise Polyphonic Representations

Video 12a: Painting Emotions in Music and Text

Video 32a: Tipping the Iceberg

Video 7c: music21 Streams, Corpus, and Meter Features

Video 12c: Graphing and Plotting in music21

Video 3a: Introduction to Pitch Representation

AI + Open Education Initiative: AI Literacies and Evaluation

AI + Open Education Initiative: Professional Education and the Judicious Use of AI

Video 9: All There Is to Unlearn - MIT Innovation Teams

Video 5: Prototype Problems Not Products - MIT Innovation Teams

Video 1: Congratulations, You Are a Terrible Robot - MIT Innovation Teams

Video 3: Technology Isn’t What You Think It Is - MIT Innovation Teams

Introduction: How to Move Technologies from Lab to Impact - MIT Innovation Teams

Video 2: All Great Ideas Start Out Bad - MIT Innovation Teams

Video 7: Lessons From a Real Garage - MIT Innovation Teams

Video 10: Go Combinatorial - MIT Innovation Teams

Video 6: Don’t Start Small, Start With What You Have - MIT Innovation Teams

Video 4: Problems Are Not Catastrophes - MIT Innovation Teams

Video 8: Are You Sure That’s a Risk? - MIT Innovation Teams

07. EdTech Before the Internet

09. Massive Open Online Courses (MOOCs)

10. Intelligent Tutors

14. Learning Games