隨機微積分

Stochastic calculus is one of the great advancements of modern probability. On the other hand, stochastic calculus is a prerequisite to understand modern mathematical finance literature. This introductory course will offer the opportunity for undergraduate (and graduate) students to open the interesting and important field for further study in advanced probability or mathematical finance. For this course, the students assume a good knowledge in linear algebra, multivariate calculus, advanced calculus and undergraduate probability. Prior knowledge of measure theory can be helpful but is not assumed for this course. Syllabus : • Basic Notions of Probability (one week) • Gaussian Processes (2 weeks) • Properties of Brownian Motion (one week) • Martingales (2 weeks) • Itô Calculus (2 weeks) • Multivariate Itô Calculus (one week) • Itô Processes and Stochastic Differential Equations (2 weeks) • Applications to Mathematical Finance (2 weeks)

calculus, advanced calculus, linear algebra and undergraduate probability

Quiz I: 60 points Midterm exam 120 points Quiz II: 60 points Final exam : 120 points

A first course in stochastic calculus by Louis-Pierre Arguin, American Mathematical Society, 2022