The Chinese University of Hong Kong (Shenzhen)
Master of Science Program in Financial Engineering
2015/2016 Fall Term
1. Course Identity
Course code
Course title (English)
Course title (Chinese)
Units
Description (English)
Description (Chinese)
MFE5110
Stochastic models
随机模型
3
This course introduces basic techniques for modelling and analysing
systems in the presence of uncertainty. It will cover Poisson processes,
Discrete and Continuous Markov chains, Martingales, Brownian
motions, Stochastic Calculus and applications in financial engineering.
本课程介绍在不确定因素影响下系统建模和分析的基本技术。内容
包括 Poisson 过程，离散和连续时间 Markov 链，鞅过 程 论 ，
Brownian 运动，随机积分及其在金融工程中的应用。
2. Lecturer
Name: Nan Chen (陈南)
Email: nchen@se.cuhk.edu.hk
Phone: +852-39438237
Office: TBA
Office hours: 12pm to 1pm, every Wed or by appointments
3. Prerequisites / Co-requisites
University level linear algebra, calculus, probability theory, or MAT1040 and its
equivalence.
4. Learning Outcomes
Upon completing this course, the student will be able to:
 Understand fundamental concepts in stochastic models;
 Obtain knowledge about Markov chains, Poisson processes, martingales,
Brownian motion, and stochastic calculus;
 Acquire some basic techniques to use the tools of stochastic processes to establish
proper models for financial problems and to perform quantitative analysis.
5. Course Syllabus
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Discrete Markov chains
Poisson processes and their applications
Continuous-time Markov chains
Martingale theory
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Brownian motion
Introduction to stochastic calculus and its financial applications
6. Assessment Scheme
Component/ method
Assignments
Midterm Examination
Final Examination
% weight
40%
30%
30%
7. Feedback for evaluation
In-class Course and Teaching Evaluation
Off-class feedbacks to instructor and/or teaching assistant
Program review
8. Reading
A. Required
1. Sheldon M. Ross, Introduction to Probability Models, 11th Edition, Academic
Press, Oxford, 2014. (Ch. 4, 5, 6, 10.1-10.5)
2. Steven E. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models,
Springer, New York, 2004. (Ch. 1-4, 6)
3. Lecturer’s notes (Available at: www.se.cuhk.edu.hk/nchen/mfe5110/)
B. Recommended
1. Rick Durrett, Probability: Theory and Examples, 4th Edition, Cambridge
University Press, Cambridge, UK, 2010.
2. Olav Kallenberg, Foundations of Modern Probability, Springer, New York, 1997.
3. Samuel Karlin and Howard M. Taylor, A First Course in Stochastic Processes, 2nd
Edition, Academic Press, San Diego, 1975.
4. Bernt Oksendal, Stochastic Differential Equations: An Introduction with
Applications, Springer, New York, 2003.
5. Sidney I. Resnick, Adventures in Stochastic Processes, Springer, 1992.
6. Sheldon M. Ross, Stochastic Processes, 2nd Edition, Wiley, New York, 1996.
7. 钱敏平，龚光鲁，陈大岳，章复熹，应用随机过程，高等教育出版社，2011.
8. 龚光鲁，随机微分方程引论，第二版，北京大学出版社，1995.
9. Course components
Activity
Lectures
Tutorials
Hours/week
3 hours per week
1 hour per week
10. Indicative teaching plan
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Content/ topic/ activity
Markov chains I: transition matrix, Chapman-Kolmogrov equations
Markov chains II: limiting probabilities and some applications
Poisson processes I: exponential distributions, Poisson process and its properties
Poisson processes II: compound Poisson process, stochastic intensity, Hawkes
processes, stochastic thinning
Continuous-time Markov chains I: birth-death processes, Kolmogrov
backward/forward equations
Continuous-time Markov chains II: limiting probabilities, uniformization
Midterm Examination
Martingale: definition and examples, stopping times, optional sampling theorem and
its application
Brownian motions I: scaled random walk and its limiting process, properties of BM,
quadratic variations
Brownian motions II: first passage time, reflection principle and the maxima of BM
Stochastic calculus I: Ito integral and its properties, Ito-Doeblin formula
Stochastic calculus II: multivariate stochastic calculus, recognition of BM, stochastic
differential equations
Stochastic calculus III: Feynman-Kac theorems, Black-Scholes option pricing theory
Final Examination