AMAT 601.20 L01 (Fall 2010)
"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: MS527&MS522

Lectures schedule (L01)
Tuesday/Thursday/Friday: 1pm/8am/1pm, MS527/MS527/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: 1:00pm, Monday, September 13, 2010
A# 1: Oct 5, Mon, 1:50pm (MS522)
  A# 2: Oct 22, Fri, 1:50pm (MS522)
   A# 3: Nov 5, Fri, 1:50pm  (MS522)
   A# 4: Nov 23, Mon , 1:50pm (MS522)
A#5
: Dec 7, Mon, 1:50pm  (MS522)
  Last day of class: December 10, Fri, 2010.
 
Project Due:
Thu, December 16, noon, MS552
Recommended textbooks:
Levy Processes and Stochastic Calculus by David Applebaum,
Cambridge University Press, 2003

Other Useful 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.
Some 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-http://math.ucalgary.ca/courses.
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_20F10.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 AMAT601.20F10:
Assignments (5)
50%=5x10% (10% for each assignments)
A1:Oct 5; A2:Oct 22; A3:Nov 5; A4:Nov 23; A5: Dec 7
Project 50% Thu, December 16 (noon), MS522

Tentative Lectures Schedule for AMAT601.20F10
Month
Day
Tuesday (MS527)
Day
Thursday(MS527)
Day
Friday (MS522)
Sept
14
Lec1:  Overview.
16
Lec2: Review of Measure and Probability
17
Lec3: Infinite Divisibility
Sept
21
Lec4: The Levy-Khintchine Formula
23
Lec5: Stable Random Variables
24
Lec6:  Levy Processes
 Sept-Oct
28
Lec7:  Subordinators 30
Lec8:  Simulation of LP I
(Dr. T. Ware's presentation at the Lab)
1
Lec9: Simulation of LP II
Oct
5
Lec10: Martingales
Appendix: Cadlag Functions
7
Lec11: Stopping Times 8
Lec12: The Jumps of Levy Processes I
Oct
12
Lec 13. The Jumps of Levy Processes I 14
Lec14:  Poisson Integration 15
Lec15: The Levy-Ito Decomposition 
Oct
19
Lec16:  Levy Processes and Semimartingales 21
Lec17:  Markov Processes (MP) and LP as MP 22
Lec18: Semigroups and their Generators
Oct
26
Lec19:  Semigroups and Generatos of Levy Processes 28
Lec20:  Stochastic Integration  29
Lec21: Stochastic Integrals Based on Levy Processes
Nov
2
Lec22: Ito Formula for LP 4
Lec23:Quadratic Variation and Ito Product Formula  5
Lec24: Stochastic Exponentials
Nov
9
Lec25:  Exponential Martingales 11
Reading Day (No Lecture) 12
Reading Day (No Lecture)
Nov
16
Lec26: Change of Measure-Girsanov's Theorem 18
Lec27: Levy Processes and Mathematical Finance I 19
Lec28: Levy Processes and Mathematical Finance II
Nov
23
Lec29: Levy Processes and Mathematical Finance III 25
Lec30: Levy Processes and Mathematical Finance III 26
Lec31: Stochastic Differential Equations (SDEs) Driven by LP  I 
Nov-Dec
30
Lec32:  SDEs  Driven by LP II 2
Lec33: SDEs Driven by LP  III 3
Lec34:  SDEs Driven by LP IV
Dec
7
Lec35: Feynman-Kac Formula and the Martingale Problem for LP 9
Lec36: Time-Change by an Independent Subordinator: LP as a Time-Change Brownian Motion 10
Lec37:  Other Applications of LP: Number Theory and Relativity


Announcements: 


Your Final Marks are Available Now. Send me e-mail to know your mark.

Projects in Levy Processes: Due-Thu, December 16, 12pm(Noon) (MS552)



Assignment#5: Due-Tue, Dec 7, 2010 (in-class, MS527)

Assignment#4: Due-Tue, Nov 23, 2010 (in-class, MS527)
Assignment#3: Due-Fri, Nov 5, 2010 (in-class, MS522)

Assignment#2: Due-Fri, Oct 22, 2010 (in-class, MS522)
Assignment#1: Due-Tue, Oct 5, 2010 (in-class, MS527)

Assignment Policy

This page was updated on December 20, 2010