Lectures

Here you will find the lectures of the course.

Here you find the introduction.
The first three chapters reviewing basics on measure theory, probability theory and stochastic processes: Chap1, Chap2 and Chap3
In Chap4 we review basics of It? integration.
In Chap5 we introduce a financial market model based on It? processes.
In Chap6 we introduce the notion of infinitely divisible distributions.
In Chap7 we introduce Lévy processes.
In Chap8 we use martingale theory to study certain properties of Lévy processes.
In Chap9 we introduce Poisson random measures and provide the Lévy-It? decomposition.
In Chap10 we introduce the stochastic integration with respect to martingale valued measures and, in particular, with respect to Lévy processes.
In Chapter11 we discuss the It? formula and some of its applications.
In Chapter12 we introduce the stochastic exponential and discuss its connection to changes of measure.
In Chapter13 we introduce a financial market model based on It?-Lévy processes.

Published Jan. 29, 2024 11:35 AM - Last modified Apr. 29, 2024 10:53 AM