Introduction 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
In 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
This 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
Introduction to the mathematical theory of stochastic calculus: construction of stochastic Ito integral, proof of Ito formula, introduction to stochastic differential equations, Girsanov theorem and F
This 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
This course focuses on dynamic models of random phenomena, and in particular, the most popular classes of such models: Markov chains and Markov decision processes. We will also study applications in q
This course provides a detailed presentation of the standard models for the valuation and hedging of derivatives products such as European options, American options, forward contracts, futures contrac
