Stochastic Calculus (2019/2020)

Course code
4S008268
Name of lecturer
Luca Di Persio
Coordinator
Luca Di Persio
Number of ECTS credits allocated
6
Academic sector
MAT/06 - PROBABILITY AND STATISTICS
Language of instruction
English
Period
II semestre dal Mar 2, 2020 al Jun 12, 2020.

Lesson timetable

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Learning outcomes

This course will provide an introduction to the theory of Stochastic Differential Equations (SDEs), mainly based on the Brownian motion type of noise. The purpose of this course is to introduce and analyse probability models that capture the stochastic features of the system under study to predict the short and long term effects that this randomness will have on the systems under consideration. The study of probability models for continuous-time stochastic processes involves a broad range of mathematical and computational tools. This course will strike a balance between the mathematics and the applications. The main applications will be mathematical finance, biology and populations evolution, also with respect to their descriptions in terms of the associated SDEs. Topics include: construction of Brownian motion; martingales in continuous time; stochastic integral; Ito calculus; stochastic differential equations; Girsanov theorem; martingale representation; the Feynman-Kac formula and Lévy processes.

Reference books
Author Title Publisher Year ISBN Note
I. Karatzas and S. Shreve Brownian motion and stochastic calculus  
D. Revuz and M. Yor Continuous martingales and Brownian motion  
B. Øksendal Stochastic Differential Equations  
N. Ikeda and S. Watanabe Stochastic Differential Equations and Diffusion Processes  
P. Protter Stochastic integration and differential equations