Episode Details
Back to Episodes
Lecture 5: Probability Theory (cont.); Stochastic Processes I
Description
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
Principal Components Analysis (PCA) is a statistical technique that transforms a random vector in a multidimensional space by shifting and rotating coordinates to identify orthogonal directions of maximum variability, often used in financial data to simplify complex covariance structures. Additionally, the discussion covers foundational probability concepts such as the Central Limit Theorem, utility optimization in asset pricing, and introduces stochastic processes like martingales, highlighting their importance in modeling financial markets and solving probability problems.
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