AMAT 601.20 L01 (Fall 2008)
"Introduction to Levy Processes with Applications"
Course Outline
Instructor:
Anatoliy Swishchuk
E-mail: aswish@ucalgary.ca
Office: MS552
Tel.: (403) 220-3274
Office Hours: TR:11:00am-11:50am

Place: MS522
Lectures Schedule for  AMAT601.20
Lectures schedule (L01)
Monday/Wednesday/: 11:00-11:50 Friday: 13:00-13:50  (MS522)

Syllabus
Definition, properties and examples of Levy Processes (LP).
Construction of LP, popular models.
Levy-Khintchine formula and Levy-Ito decomposition of LP. 
Simulation of LP.
Applications of LP to finance, operator, semigroups, relativistic and number theories.

Course Information Sheet
 Important Class Dates:
First day of class: 11:00am, Monday, September 8, 2008
   A# 1: Sept 29, Mon, 11:00-11:50 (MS522)
  A# 2: Oct 15, Wed, 11:00-11:50 (MS522)
  A# 3: Oct 29, Wed, 11:00-11:50 (MS522)
   A# 4: Nov 17, Mon, 11:00-11:50 (MS522)
   A#5: Dec 3, Wed, 11:00-11:50am (MS522)
  Last day of class: December 5, Fri, 2008.
 
Project Due:
Mon, December 8, noon, MS552
Recommended textbooks:
Levy Processes and Stochastic Calculus by David Applebaum,
Cambridge University Press, 2003
Levy Processes and Infinitely Divisible Distributions by Ken-Iti Sato, Cambridge University Press,1999
Other books on Levy Processes:
Levy Processes in Finance. Pricing Financial Derivatives
by Wim Schoutens, Wiley, 2003
Financial Modelling with Jump Processes by Rama Cont and Peter Tankov, Chapman and Hall/CRC Financial Mathematics Series,2004
Levy Processes by Bertoin J., Cambridge University Press, 1996.
Useful papers on Levy Processes:
An introduction to Levy processes with applications in finance, Antonis Papapantoleon, 2008
An introduction to the theory of Levy processes, Andreas Kyprianou, (first two chapters of Introductions of Levy Processes with Applications by Kuprianou A., Springer 2006)
Change of time and measure for Levy processes, Cherny A. and Shiryaev A., August 2002.
Levy Processes in Finance: Theory, Numerics and Empirical facts, S. Raible, PhD Thesis, University of Frieburg, 2000.


Course Web Page:
The current official syllabus for this course is available in the wall pockets across from MS 476 and
on the webpage at www.math.ucalgary.ca Course Listing-Undergraduate (http://math.ucalgary.ca/courses/f08).
There is also a web page for this course which contains the course outline, tentative course schedule,  grading scheme, important class dates, etc.
Announcements made in class will be posted there (see end of this web-page). The address of this web page is: http://www.math.ucalgary.ca/~aswish/amat601_20F08.html/

Class work:
In-class lectures with typical examples (lecture notes will be posted on the webpage in the form of pdf-files
);
your computer must have an Adobe Acrobat reader (for free downloading see www.adobe.com).

Assignments and Project
There will be 5 Assignments and 1 Project

Grading scheme (Course Evaluation) for AMAT601.20F08:
Assignments (5)
50%=5x10% (10% for each assignments)
A1:Sept 29; A2:Oct 15; A3:Oct 29; A4:Nov 17; A5:Dec 3
Project 50% Mon, December 8 (noon)

Tentative Lectures Schedule for AMAT601.20F08
Month
Day
Monday
Day
Wednesday
Day
Friday
Sept
8
Lec1:  Overview.
10
Lec2: Review of Measure and Probability
12
Lec3: Infinite Divisibility
Sept
15
Lec4: The Levy-Khintchine Formula
17
Lec5: Stable Random Variables
19
Lec6:  Levy Processes
 Sept
22
Lec7:  Subordinators 24
Lec8:  Simulation of LP I
(Dr. T. Ware's presentation at the Lab)
26
Lec9: Simulation of LP II
Sept-Oct
29
Lec10: Martingales
Appendix: Cadlag Functions
1
Lec11: Stopping Times 3
Lec12: The Jumps of Levy Processes
ct
6
Lec13:  Poisson Integration 8
Lec14: The Levy-Ito Decomposition  10
Lec15:  Levy Processes and Semimartingales
Oct
13
Thanksgiving Day (No Lectures) 15
Lec16:  Markov Processes (MP) and LP as MP 17
Lec17: Semigroups and their Generators
Oct
20
Lec18:  Semigroups and Generatos of Levy Processes 22
Lec19:  Stochastic Integration  24
Lec20: Stochastic Integrals Based on Levy Processes
Oct
27
Lec21: Ito Formula for LP 29
Lec22:Quadratic Variation and Ito Product Formula  31
Lec23: Stochastic Exponentials
Nov
3
Lec24:  Exponential Martingales 5
Lec25: Change of Measure-Girsanov's Theorem 7
Lec26: Levy Processes and Mathematical Finance I 
Nov
10
Reading Day (No Lectures)
12
Lec27: Levy Processes and Mathematical Finance II 14
Lec28: Levy Processes and Mathematical Finance III
Nov
17
Lec29: Levy Processes and Mathematical Finance IV 19
Lec30: Stochastic Differential Equations (SDEs) Driven by LP  I  21
Lec31:  SDEs  Driven by LP II
Nov
24
Lec32: SDEs Driven by LP  III 26
Lec33:  SDEs Driven by LP IV 28
Lec34: Feynman-Kac Formula and the Martingale Problem for LP
Dec
1
Lec35: Time-Change by an Independent Subordinator: LP as a Time-Change Brownian Motion 3
Lec36:  Other Applications of LP: Number Theory and Relativity 5
Lec37: Course Review

Announcements: 

Your marks for project and course are available now.
Send me e-mail to know your mark.


General Guidelines for Grades

This page was updated on December 11, 2008.