amat601_20F08

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

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).

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)

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