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 Uploaded 03-12-25 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. Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices