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Probability Modelling and Applications (MATH3029)

                                                                                                           

Lecturer:   Dr. Alex Szimayer
Time:   2 pm - 4 pm, Thursday,  20 July, 2006 ~ 26 October, 2006
Venue:   Mathematical Sciences Institute, ANU
Textbook:  

Nil.  Lecture notes only.
Ref. book:   Bauer, Heinz (2001) Measure & Integration Theory. de Gruyter, Berlin & New York.   (Amazon)
Jacod, Jean and Protter, Philip (2004) Probability Essentials . Springer, Berlin & Heidelberg.   (Amazon)
Form:   Lectures
Web Site:   ANU Course Site (change 2007 to 2006)

Outline: (copied from here) 

The course Probability Modelling and Applications (MATH3029) introduces stochastic processes with a view towards applications in fields such as finance, insurance, risk management, and operations research.

The course aims to provide mathematics students with basic knowledge of stochastic processes where practical rather than theoretical aspects are emphasized. The course contains sufficient material for students to feel comfortable with Markov chains, Poisson processes, and Brownian motion, and the conceptual formulation of topics in continuous time finance, insurance and risk management, where these processes are applied. Also the concept of martingales, which is fundamental for understanding the modern option pricing theory of Black and Scholes, is introduced.

Probability Modelling and Applications provides a sound foundation to progress to honours and post-graduate courses emphasizing the theory of mathematical finance and stochastic analysis.

Assignments:

 No.

Due Date

 Contents

Link (Latex from Assignment 7)

1

27 July, 2006

 Generating Function, branching process Assignment 1

2

 3 August, 2006 Large sample approximation, use of gf Assignment 2

3

 10 August, 2006 Markov Chain 1 Assignment 3

4

 17 August, 2006 Markov Chain 2 Assignment 4

5

 24 August, 2006 Probability Space Assignment 5

6

 31 August, 2006 Distribution function, Lebesgue measure Assignment 6
7 21 Sept., 2006 Random variable, Expectation Basics Assignment 7
8 28 Sept., 2006 More Expectation, Fatou's Lemma Assignment 8
9 5 October, 2006 Independent random variables Assignment 9
10 12 October, 2006 Characteristic Function, Convergence Assignment 10
11 19 October, 2006 Weak Converge, Central Limit Theorem Assignment 11
12 26 October, 2006 Brownian Motion and Black & Scholes Assignment 12
 		      

Other useful resources:

There are lecture notes,  tutorial notes, assignments, reference solutions, available (which are prepared by the lectures).  If you want to have a look, send me an email and cc to Dr. Alex Szimayer.  Ref my notes here.