Spring 2019  STAT 832 G200
Applied Probability Models (4)
Class Number: 8499
Delivery Method: In Person
Overview

Course Times + Location:
Tu, Th 10:30 AM – 11:20 AM
AQ 5025, Burnaby

Instructor:
JeanFrancois Begin
jbegin@sfu.ca
778.782.4478
Office: SCK10548
Description
CALENDAR DESCRIPTION:
Application of stochastic processes: queues, inventories, counters, etc. Reliability and life testing. Point processes. Simulation. Students with credit for STAT 870 may not take this course for further credit.
COURSE DETAILS:
This course is divided into fourteen chapters. The three last chapters will be covered if time allows.
 Chapter 1, Probabilistic Foundations : Sample Space, Random Variable, Probability Measure, Distribution, SigmaAlgebra, Measurable Space, Probability Triple.
 Chapter 2, Stochastic Processes : Stochastic Process, Filtration, Stopping Time.
 Chapter 3, Expectations : Independence, Conditional Probability, Expectation, Moments, Conditional Expectation.
 Chapter 4, Martingales : Definition, Examples, Stopped Process, Optional Stopping Theorem, Markov Process.
 Chapter 5, Introduction to DiscreteTime Market Models : Price Processes, Measurable Space, Arbitrage, Pricing, TwoPeriod Generalization.
 Chapter 6, Advanced DiscreteTime Market Models : Price Systems and Martingale Measures, SelfFinancing Strategy and Arbitrage, Arbitrage and Martingale Measures, Attainable Claims and Price Uniqueness, Admissible Strategy and Martingales, Relationship Between Replication and Pricing, RiskNeutral and Martingale Measures, Market Completeness.
 Chapter 7, Convergence : Metric Spaces, Almost Sure Convergence, Convergence in Probability, Convergence in Mean, Convergence in Distribution
 Chapter 8, Brownian Motion : Normal Distribution Review, Scaled Random Walks, Brownian Motion, Construction of the Brownian Motion.
 Chapter 9, Stochastic Integral : Riemann Integration, Ito Integration.
 Chapter 10, Stochastic Differential Equations and It¯o’s Lemma : Ordinary Differential Equations, Ito’s Lemma, Product Rule, Multidimensional Ito’s Lemma, Solutions of Stochastic Differential Equations.
 Chapter 11, Girsanov’s Theorem and Change of Measures : Change of Measure, RadonNikodym Theorem, Girsanov’s Theorem, Multidimensional Girsanov’s Theorem.
 Chapter 12, Replication Strategies and Martingale Representation Theorem : SelfFinancial Strategies, Martingale Representation Theorem, Asset Replication.
 Chapter 13, Introduction to Jump Processes : Poisson Process, Compound Poisson Process, Jump Processes and Their Integrals, Stochastic Calculus for Jump Processes, Asset Driven by a Jump Model.
 Chapter 14, Simulation : Exact Methods, Discretization, Market Models.
Grading
 InClass Activities 20%
 Midterm Exam 40%
 Final Exam 40%
NOTES:
Above grading is subject to change.
Materials
RECOMMENDED READING:
 Hull, J. C. (2015). Options, Futures, and Other Derivatives, 9th ed. Pearson.
 Lyaso, A. (2017). Stochastic Methods in Asset Pricing. The MIT Press.
 McDonald, R. L. (2015). Derivatives Markets, 3rd ed. Pearson.
 Shreve, S. (2004). Stochastic Calculus for Finance I : The Binomial Asset pricing Model. Springer Science & Business Media.
 Shreve, S. (2004). Stochastic Calculus for Finance II : ContinuousTime Models. Springer Science & Business Media.
Graduate Studies Notes:
Important dates and deadlines for graduate students are found here: http://www.sfu.ca/deangradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.
Registrar Notes:
SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.
Each student is responsible for his or her conduct as it affects the University community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s1001.html
ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS