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

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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 This final lecture provides an in-depth discussion of Itô’s formula and its generalizations, illustrating how it applies to functions of Brownian motion, especially in finance for modeling derivative pricing and geometric Brownian motion. It also explains the derivation of the Black-Scholes differential equation through risk-neutral hedging, the solution of the heat (diffusion) equation as a fundamental tool for solving such PDEs, and introduces more advanced stochastic differential equations like the Ornstein-Uhlenbeck process, emphasizing their broad applications beyond 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.

Published 2025-12-03 · Watch on YouTube ↗
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