COM-417: Advanced probability and applicationsIn this course, various aspects of probability theory are considered. The first part is devoted to the main theorems in the field (law of large numbers, central limit theorem, concentration inequaliti
MATH-330: Martingales and Brownian motionIntroduction to the theory of discrete-time martingales including, in particular, the convergence and stopping time theorems. Application to branching processes. Introduction to Brownian motion and st
MATH-476: Optimal transportThe first part is devoted to Monge and Kantorovitch problems, discussing the existence and the properties of the optimal plan. The second part introduces the Wasserstein distance on measures and devel
MATH-470: Martingales in financial mathematicsThe aim of the course is to apply the theory of martingales in the context of mathematical finance. The course provides a detailed study of the mathematical ideas that are used in modern financial mat
ENG-639: Dynamic programming and optimal controlThis course provides an introduction to stochastic optimal control and dynamic programming (DP), with a variety of engineering
applications. The course focuses on the DP principle of optimality, and i
PHYS-467: Machine learning for physicistsMachine learning and data analysis are becoming increasingly central in sciences including physics. In this course, fundamental principles and methods of machine learning will be introduced and practi
FIN-415: Probability and stochastic calculusThis course gives an introduction to probability theory and stochastic calculus in discrete and continuous time. The fundamental notions and techniques introduced in this course have many applicatio
EE-715: Optimal controlThis doctoral course provides an introduction to optimal control covering fundamental theory, numerical implementation and problem formulation for applications.
