Introduction to Stochastic Analysis
Term 1, 2023
Cricos Provider Code: 00098G
Page | 2
Staff
Position Name Email Room
Lecturer-in-charge Dr Libo Li libo.li@unsw.edu.au RC-1035
Please refer to your Timetable on MyUNSW for your Lecture Tut, Lab enrolment days and times.
Timetable weblink: http://timetable.unsw.edu.au/2023/MATH5975.html
Administrative Contacts
Please visit the School of Mathematics and Statistics website for a range of information on School
Policies, Forms and Help for Students.
For information on Courses, please go to “Current Students” and either Undergraduate and/or
Postgraduate”, Course Homepage” for information on all course offerings,
The “Student Notice Board” can be located by going to the “Current Students” page; Notices are
posted regularly for your information here. Please familiarise yourself with the information found
in these locations. The School web page is: https://www.maths.unsw.edu.au
If you cannot find the answer to your queries on the web you are welcome to contact the Student
Services Office directly.
By email Postgraduate pg.mathsstats@unsw.edu.au
By phone: 9385 7053
Should we need to contact you, we will use your official UNSW email address of in the first
instance. It is your responsibility to regularly check your university email account. Please state
your student number in all emails.
Page | 3
Course Information
Course Aims
Modern theory of financial markets relies on advanced mathematical and statistical methods that
are used to model, forecast and manage risk in complex financial transactions. After the
publication in 1973 of the ground-breaking paper of Black and Scholes on the arbitrage pricing of
European call options, it became clear that Stochastic Analysis is an indispensable tool for the
theory of financial markets, derivation of prices of standard and exotic options and other derivative
securities, hedging related financial risk, as well as managing the interest rate risk.
In this course, you will learn the basic concepts and techniques of Stochastic Analysis, such as:
Brownian motion, martingales, Ito stochastic integral, Ito's formula, stochastic differential
equations, equivalent change of a probability measure, integral representation of martingales with
respect to a Brownian filtration, relations to second order partial differential equations, the
Feynman-Kac formula, and stochastic processes with discontinuities.
The course consists of theorems and proofs. The main goal of the course is to provide a
necessary mathematical background for MATH5816 Continuous Time Financial Modelling and
MATH5985 Term Structure Modelling, rather than to focus directly on financial concepts.
Course Description
Modern theory of financial markets relies on advanced mathematical statistical methods that are
used to model, forecast and manage risk in complex financial transactions. After publication in
1973 of the ground-breaking paper of Black and Scholes on the arbitrage pricing of European call
options, Stochastic Analysis became an indispensable tool for the theory of financial markets,
derivation of prices of standard and exotic options and other derivative securities, hedging related
financial risk, as well as managing the interest rate risk. In this course, you will learn the basic
concepts and techniques of Stochastic Analysis, such as: Brownian motion, Ito stochastic integral,
Ito's formula, changes of measures, stochastic differential equations, and their relations to second
order partial differential equations, and Feynman-Kac formula.
Page | 4
Assessment and Deadlines
Assessment Week Weighting
%
Due date if applicable Course Learning
Outcome (CLO)
Assignment 1 Week 4 5% Due week 4 CLO1, CLO2, CL03
Midterm Test Week 7 20% Due week 7 CLO1, CLO2, CLO3
Assignment 2 Week 10 15% Due week 10 CLO1, CLO2, CLO3
Final Exam 60% UNSW Exam Period All
Late Submission of Assessment Tasks
No late submissions will be accepted. (Where "late" in this context means after any extensions
granted for Special Consideration or Equitable Learning Provisions.)
Course Learning Outcomes (CLO)
1. Recognise which analysis procedure is appropriate for a given research problem.
2. Apply probability theory and stochastic analysis to practical problems.
3. Demonstrate an understanding of the usefulness of Stochastic Analysis in your
professional area.
Course Schedule
The course will include material taken from some of the following topics. This is should only serve
as a guide as it is not an extensive list of the material to be covered and the timings are
approximate. The course content is ultimately defined by the material covered in lectures; refer to
Moodle for Lecture notes.
Weeks Topic
1 Basic Probability, Conditional Expectation
2 Stopping Times, Discrete Time Martingales
3 Continuous Time Martingale, Brownian Motion,
4 Stochastic Integrals
5 Ito's Formula
7 Continuous Semimartingales
8 Stochastic Differential Equation
Page | 5
9 Radon Nikodym Density and Girsanov Theorem
10 Feynman-Kac Formula
Moodle
Log in to Moodle to find announcements, general information, notes, lecture slide, classroom
tutorial and assessments etc.
https://moodle.telt.unsw.edu.au
School and UNSW Policies
The School of Mathematics and Statistics has adopted a number of policies relating to enrolment,
attendance, assessment, plagiarism, cheating, special consideration etc. These are in addition to
the Policies of The University of New South Wales. Individual courses may also adopt other
policies in addition to or replacing some of the School ones. These will be clearly notified in the
Course Initial Handout and on the Course Home Pages on the Maths Stats web site.
Students in courses run by the School of Mathematics and Statistics should be aware of the School
and Course policies by reading the appropriate pages on the Maths Stats web site starting at:
https://www.maths.unsw.edu.au/currentstudents/assessment-policies
The School of Mathematics and Statistics will assume that all its students have read and
understood the School policies on the above pages and any individual course policies on the
Course Initial Handout and Course Home Page. Lack of knowledge about a policy will not be an
excuse for failing to follow the procedure in it.
Academic Integrity and Plagiarism
UNSW has an ongoing commitment to fostering a culture of learning informed by academic
integrity. All UNSW staff and students have a responsibility to adhere to this principle of academic
integrity. Plagiarism undermines academic integrity and is not tolerated at UNSW. Plagiarism at
UNSW is defined as using the words or ideas of others and passing them off as your own.
The UNSW Student Code provides a framework for the standard of conduct expected of UNSW
students with respect to their academic integrity and behaviour. It outlines the primary
Page | 6
obligations of students and directs staff and students to the Code and related procedures.
In addition, it is important that students understand that it is not permissible to buy
essay/writing services from third parties as the use of such services constitutes plagiarism
because it involves using the words or ideas of others and passing them off as your own. Nor is
it permissible to sell copies of lecture or tutorial notes as students do not own the rights to this
intellectual property.
If a student breaches the Student Code with respect to academic integrity, the University may take
disciplinary action under the Student Misconduct Procedure.
The UNSW Student Code and the Student Misconduct Procedure can be found at:
https://student.unsw.edu.au/plagiarism
An online Module “Working with Academic Integrity” (https://student.unsw.edu.au/aim) is a six-
lesson interactive self-paced Moodle module exploring and explaining all of these terms and
placing them into your learning context. It will be the best one-hour investment you’ve ever made.
Plagiarism
Plagiarism is presenting another person's work or ideas as your own. Plagiarism is a serious
breach of ethics at UNSW and is not taken lightly. So how do you avoid it? A one-minute video for
an overview of how you can avoid plagiarism can be found
https://student.unsw.edu.au/plagiarism.
Additional Support
ELISE (Enabling Library and Information Skills for Everyone)
ELISE is designed to introduce new students to studying at UNSW.
Completing the ELISE tutorial and quiz will enable you to:
analyse topics, plan responses and organise research for academic writing and other
assessment tasks
effectively and efficiently find appropriate information sources and evaluate relevance
to your needs
use and manage information effectively to accomplish a specific purpose
Page | 7
better manage your time
understand your rights and responsibilities as a student at UNSW
be aware of plagiarism, copyright, UNSW Student Code of Conduct and Acceptable Use of
UNSW ICT Resources Policy
be aware of the standards of behaviour expected of everyone in the UNSW community
locate services and information about UNSW and UNSW Library
Some of these areas will be familiar to you, others will be new. Gaining a solid understanding of all
the related aspects of ELISE will help you make the most of your studies at UNSW.
The ELISE training webpages:
https://subjectguides.library.unsw.edu.au/elise/aboutelise
Equitable Learning Services (ELS)
If you suffer from a chronic or ongoing illness that has, or is likely to, put you at a serious
disadvantage, then you should contact the Equitable Learning Services (previously known as
SEADU) who provide confidential support and advice.
They assist students:
living with disabilities
with long- or short-term health concerns and/or mental health issues
who are primary carers
from low SES backgrounds
of diverse genders, sexes and sexualities
from refugee and refugee-like backgrounds
from rural and remote backgrounds
who are the first in their family to undertake a bachelor-level degree.
Their web site is: https://student.unsw.edu.au/els/services
Equitable Learning Services (ELS) may determine that your condition requires special
arrangements for assessment tasks. Once the School has been notified of these, we will make
every effort to meet the arrangements specified by ELS.
Additionally, if you have suffered significant misadventure that affects your ability to complete the
course, please contact your Lecturer-in-charge in the first instance.
Page | 8
Academic Skills Support and the Learning Centre
The Learning Centre offers academic support programs to all students at UNSW Australia. We
assist students to develop approaches to learning that will enable them to succeed in their
academic study. For further information on these programs please go to:
http://www.lc.unsw.edu.au/services-programs
Applications for Special Consideration for Missed Assessment
Please adhere to the Special Consideration Policy and Procedures provided on the web page
below when applying for special consideration.
https://student.unsw.edu.au/special-consideration
Please note that the application is not considered by the Course Authority, it is considered by a
centralised team of staff at the Nucleus Student Hub.
The School will contact you (via student email account) after special consideration has been
granted to reschedule your missed assessment, for a lab test or paper-based test only.
For applications for special consideration for assignment extensions, please note that the new
submission date and/or outcome will be communicated through the special consideration web
site only, no communication will be received from the School.
For Dates on Final Term Exams and Supplementary Exams please check the “Key Dates for
Exams” ahead of time to avoid booking holidays or work obligations.
https://student.unsw.edu.au/exam-dates
If you believe your application for Special Consideration has not been processed, you should email
specialconsideration@unsw.edu.au immediately for advice.
Course Evaluation and Development (MyExperience)
Student feedback is very important to continual course improvement. This is demonstrated within
the School of Mathematics and Statistics by the implementation of the UNSW online student
Page | 9
survey myExperience, which allows students to evaluate their learning experiences in an
anonymous way. myExperience survey reports are produced for each survey. They are released to
staff after all student assessment results are finalised and released to students. Course
convenor will use the feedback to make ongoing improvements to the course.