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MATH5975 Introduction to Stochastic Analysis
创建日期：2024-05-20 18:06:17
所属分类：数学mathematics
标签： MATH5975
Introduction to Stochastic Analysis

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MATH5975

Introduction to Stochastic Analysis

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,


If you cannot find the answer to your queries on the web you are welcome to contact the Student
Services Office directly.

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
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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
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 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.

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

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