AMATSTAT 601_24 L01 (Winter 2013)
"Diffusion, Markov Processes and Martingales"
Course Outline
Instructor:
Anatoliy Swishchuk
E-mail: aswish@ucalgary.ca
Office: MS552
Tel.: (403) 220-3274
Office Hours: TR:11:00am-11:50am

Place: MS365

Lectures schedule (L03)
Monday/Wednesday/Friday: 9:00-9:50am, MS365

Syllabus

Course Information Sheet

 Important Class Dates:
First day of class: 9:00am, Wednesday, January 9, 2013
A# 1: Jan 28, Mon, 9:50am (MS365)
  A# 2: Feb 25, Mon, 9:50am (MS365)
   A# 3: Mar 11, Mon, 9:50am  (MS365)
   A# 4: Mar 25, Mon , 9:50am (MS365)
A#5
: Apr 15, Mon, 9:50am  (MS365)
  Last day of class: April 16, Tue, 2013.
 
Project Due:
Mon, April 22, noon, MS552

Recommended textbooks:

Rogers L.C.G. & Williams D. Diffusion, Markov Processes & Martingales. Cambridge University Press, 2000.

Other Useful Books
Ethier S. & Kurtz T. Markov Processes: Characterization and Convergence, Wiley, 1986.
Levy Processes and Stochastic Calculus by David Applebaum, Cambridge University Press, 2003
Financial Modelling with Jump Processes by Rama Cont and Peter Tankov, Chapman and Hall/CRC Financial Mathematics Series,2004

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/amatstat601_224W13.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 AMATSTAT601_24W13:
Assignments (5)
50%=5x10% (10% for each assignments)
A1:Jan 28; A2:Feb 25 22; A3:Mar 11; A4:Mar 25; A5: Apr 15
Project 50% Mon, April 22 (noon), MS552

Tentative Lectures Schedule for AMAT601.20F10
Month
Day
Wednesday
Day
Friday
Day
Monday
Jan
9
Lec1:  Intro to Stochastic Processes I
11
Lec2: Intro to Stochastic Processes II
14
Lec3: Brownian Motion (BM)
Jan
16
Lec4: BM: Continuity of Path, Maximum Value, Arccos Law
18
Lec5: Variations of BM and Extensions
21
Lec6:  Some Functionals of BM by Martingale Methods
 Jan
23
Lec7:  Applications of BM in Finance
25
Lec8:  Brownian Bridge
28
Lec9: Multi-dimensional BM
Jan-Feb
30
Lec10: Gaussian Processes
1
Lec11: Fractional BM and OU Process 4
Lec12: Martingales: Discrete Time
Feb
6
Lec 13: Martingales: Continuous Time
8
Lec14: Stopping Times, Optional Stopping Theorem, Wald's Identities 11
Lec15: Martingales in Finance (Discrete Time): (B,S)-security Market-Main Definitions
Feb
13
Lec16:  Martingales in Finance (Discrete Time): (B,S)-security Market-Options 15
Lec17:  Markov Processes (MP) 18
Reading Week (No Lectures): Feb 18-24
Monday, Jan  25: Lec 18:
Semigroups and their Generators for MP
Feb-Mar
27
Lec19:  Diffusion Processes (DP): Ito Integral 1
Lec20:  SDEs: GBM, OU & Vasicek Processes 4
Lec21: General SDEs
Mar
6
Lec22: Ito and Other Formulas 8
Lec23: Absolute Continuity and the Radon-Nikodym Theorem 11
Lec24: Girsanov's Theorem and Risk-Neutral Measure
Mar
13
Lec25:  Continuous-time (B,S)-security market (Basics)
15
Lec26: Levy Processes (LP) as MP
18
Lec27: The Levy-Khintchine Formula
Mar
20
Lec28: Properties of LP 22
Lec29: The Levy-Ito Decomposition 25
Lec30: Semigroups and Generators of LP
Mar-Apr
27
Lec31: Semigroups and Generators of LP II
29
Good Friday (No Lecture) 1
 Lec32: Martingale Problem for MP
Apr
3
Lec33: Martingale Problem for MP II
5
 Lec34:  Markov Chains (MC) 8
Lec35: Martingale Problem for MC
Apr
10
Lec36: Martingale Problem for DP 12
 Lec37: Martingale Problem for a General MP 15
Lec38: History, Ideas, Applications of Levy processes-one of the most amazing Markov processes.


Announcements: 


Projects: Due-Monday, April 22, 2013 (noon) (MS552)

List of Projects


Assignment#5: Due-Mon, Apr 15, 2013 (in-class, MS365)

Assignment#4: Due-Mon, Mar 25, 2013 (in-class, MS365)
Assignment#3: Due-Mon, Mar 11, 2013 (in-class, MS365)

Assignment#2: Due-Mon, Feb 25, 2013 (in-class, MS365)
Assignment#1: Due-Mon, Jan 28, 2013 (in-class, MS365)

Assignment Policy

This page was updated on May 6, 2013