This is a course on Probability and Stochastic Processes, having economic and financial applications in view. Accordingly, after introducing some basic notions of probability theory (including conditional expectation), lectures will focus on those processes which are popular in finance, including martingales, submartingales, Poisson process, Brownian motion and exponential martingale. As far as possible, technicalities are avoided. Various exercises and applications will be discussed as well. At the end of the course the Student will be able to deal with the basic tools of stochastic analysis necessary to attend the course of Quantitative Finance.
Course Prerequisites
The course requires basic knowledge of Mathematical Analysis (functions, derivative, integral) and of Probability (discrete and continuous random variables, expectation and variance, conditional probability). Anyway a review of basic probability will be made available before the beginning of the course.
Teaching Methods
Lectures will be given regularly on the blackboard. Additionally, tutorials will be organized every week.
Assessment Methods
The exam is written. There are multiple choice questions in the first part and then open ended questions, in which the Student will be asked to solve exercises, give some theoretical results involving definitions, properties and some proofs. Books and calculators will not be allowed in the exam. Templates of the written exam are available in the Kiro page.
Texts
Two reference books are * Brzezniak Z. and Zastawniak T. (1999). "Basic Stochastic Processes". Springer. * Grimmett G. and Stirzaker D. (2001-third edition). "Probability and random processes". Oxford. Notice that only some parts of these texts will be used. Further notes will be provided by the teacher during the course (available in the Kiro webpage).
Contents
- Random variables and vectors - Distribution functions - Transformations of random variables and vectors - Filtrations - Conditional expectation - Simple random walk (gambler's ruin problem) - Martingales, sub-martingales and super-martingales - Stopping times - Brownian motion - Poisson process - Itô integral, Itô formula (stochastic chain rule)
Course Language
English
More information
This course is a prerequisite for the course in Quantitative Finance.
