Lecture 24: Stochastic Calculus

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 provides an in-depth introduction to stochastic calculus, focusing on Brownian motion with drift and the construction of Itô integrals, which extend ordinary calculus to stochastic processes. Key concepts include the definition of Itô integrals for random and deterministic functions, the Itô isometry connecting variance and integrand norms, and Itô’s formula, which generalizes Taylor expansions to stochastic settings, enabling applications such as solving partial differential equations and martingale problems in quantitative finance. 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.