Spring 2019 - STAT 832 G200
Applied Probability Models (4)
Class Number: 8499
Delivery Method: In Person
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.
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, Sigma-Algebra, 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 Discrete-Time Market Models : Price Processes, Measurable Space, Arbitrage, Pricing, Two-Period Generalization.
- Chapter 6, Advanced Discrete-Time Market Models : Price Systems and Martingale Measures, Self-Financing Strategy and Arbitrage, Arbitrage and Martingale Measures, Attainable Claims and Price Uniqueness, Admissible Strategy and Martingales, Relationship Between Replication and Pricing, Risk-Neutral 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, Radon-Nikodym Theorem, Girsanov’s Theorem, Multidimensional Girsanov’s Theorem.
- Chapter 12, Replication Strategies and Martingale Representation Theorem : Self-Financial 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.
- In-Class Activities 20%
- Midterm Exam 40%
- Final Exam 40%
Above grading is subject to change.
- 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 : Continuous-Time Models. Springer Science & Business Media.
Graduate Studies Notes:
Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/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.
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