MATH5551: Semester 2, 2024

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Units MATH5551 Semester 2 2024 [Normal day]

Unit outline_

MATH5551: Stochastics and Finance

Semester 2, 2024 [Normal day] - Camperdown/Darlington, Sydney

Overview

Stochastics examines phenomena in which chance plays a central role. The theory of stochastic phenomena has applications in engineering systems, the physical and life sciences and economics, to give just a few examples. Applications of stochastic processes arise particularly naturally in finance where there are fluctuations in stock prices and practitioners are required to solve different types of optimisation problems in stochastically driven systems. For this reason, it is particularly important that mathematicians in general and especially mathematicians specialising in problems in the financial industry are equipped with tools to analyse and quantify random phenomena. This unit will expose you to critical topics in the theory and application of stochastic processes and analysis in mathematical finance. You will learn how to identify problems that require the application of stochastic theory, how to rigorously describe such problems using appropriate mathematical frameworks and how to tackle and solve the problem once it has been phrased in terms of stochastic theory. Along the way, you will also gain a deep knowledge about diverse topics in finance and the relevance of mathematical analysis in the financial industry.

Unit details and rules

Academic unit	Mathematics and Statistics Academic Operations
Credit points	6
Prerequisites ?	None
Corequisites ?	None
Prohibitions ?	None
Assumed knowledge ?	Students should have a sound knowledge of probability theory and stochastic processes from, for example, STAT2X11 and STAT3021 or equivalent.
Available to study abroad and exchange students	Yes

Teaching staff

Coordinator	Ben Goldys, beniamin.goldys@sydney.edu.au
Lecturer(s)	Ben Goldys, beniamin.goldys@sydney.edu.au

Assessment

The census date for this unit availability is 2 September 2024

Details
Criteria

Type	Description	Weight	Due	Length
Supervised exam ?	Final exam Four problem based questions	60%	Formal exam period	2 hours
Outcomes assessed:
Assignment	Assignment 1 Take home assignment	20%	Week 07 Due date: 15 Sep 2024 at 23:59 Closing date: 22 Sep 2024	Two weeks
Outcomes assessed:
Assignment	Assignment 2 Take home assignment	20%	Week 12 Due date: 27 Oct 2024 at 23:59 Closing date: 03 Nov 2024	Two weeks
Outcomes assessed:

Assessment summary

Assessment consists of two assignments and the final examination. If a second replacement exam is required, this exam may be delivered via an alternative assessment method, such as viva voce (oral exam). The alternative assessment will meet the same learning outcomes as the original exam. The format of the alternative assessment will be determined by the unit coordinator.

Assessment criteria

Result name	Mark range	Description
High distinction	85-100	Representing complete or close to complete mastery of the material.
Distinction	75-85	Representing excellence but substantially less than complete mastery.
Credit	65-74	Representing a creditable performance that goes beyond routine knowledge, but lees than excellence.
Pass	50-64	Representing at least routine knowledge and understanding of the most important topics and ideas of the course.
Fail	0-49	When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see guide to grades.

Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

Deduction of 5% of the maximum mark for each calendar day after the due date.
After ten calendar days late, a mark of zero will be awarded.

This unit has an exception to the standard University policy or supplementary information has been provided by the unit coordinator. This information is displayed below:

For every calendar date up to and including ten calendar days after the the date, a penalty of 5% of the maximum awardable marks will be applied to late work. For work submitted more than ten days after the due date a mark of zero will be awarded.

Academic integrity

The Current Student website provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

Use of generative artificial intelligence (AI) and automated writing tools

You may only use generative AI and automated writing tools in assessment tasks if you are permitted to by your unit coordinator. If you do use these tools, you must acknowledge this in your work, either in a footnote or an acknowledgement section. The assessment instructions or unit outline will give guidance of the types of tools that are permitted and how the tools should be used.

Your final submitted work must be your own, original work. You must acknowledge any use of generative AI tools that have been used in the assessment, and any material that forms part of your submission must be appropriately referenced. For guidance on how to acknowledge the use of AI, please refer to the AI in Education Canvas site.

The unapproved use of these tools or unacknowledged use will be considered a breach of the Academic Integrity Policy and penalties may apply.

Studiosity is permitted unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission as detailed on the Learning Hub’s Canvas page.

Outside assessment tasks, generative AI tools may be used to support your learning. The AI in Education Canvas site contains a number of productive ways that students are using AI to improve their learning.

Learning support

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

Support for students

The Support for Students Policy 2023 reflects the University’s commitment to supporting students in their academic journey and making the University safe for students. It is important that you read and understand this policy so that you are familiar with the range of support services available to you and understand how to engage with them.

The University uses email as its primary source of communication with students who need support under the Support for Students Policy 2023. Make sure you check your University email regularly and respond to any communications received from the University.

Learning resources and detailed information about weekly assessment and learning activities can be accessed via Canvas. It is essential that you visit your unit of study Canvas site to ensure you are up to date with all of your tasks.

If you are having difficulties completing your studies, or are feeling unsure about your progress, we are here to help. You can access the support services offered by the University at any time:

Support and Services (including health and wellbeing services, financial support and learning support)
Course planning and administration
Meet with an Academic Adviser

Weekly schedule

WK	Topic	Learning activity
Week 01	Overview of the main concepts from the general theory of stochastic processes.	Block teaching (4 hr)
Week 02	Overview of the main results from the Ito calculus.	Block teaching (4 hr)
Week 03	Existence and uniqueness theorem for solutions to a linear BSDE	Block teaching (4 hr)
Week 04	Existence and uniqueness theorem for a nonlinear BSDE	Block teaching (4 hr)
Week 05	Comparison properties of solutions to a BSDE	Block teaching (4 hr)
Week 06	Stochastic optimal stopping problems	Block teaching (4 hr)
Week 07	Applications to European and American options in nonlinear financial models	Block teaching (4 hr)
Week 08	Stochastic Dynkin games	Block teaching (4 hr)
Week 09	Hamilton-Jacobi-Bellman equation	Block teaching (4 hr)
Week 10	Stochastic Pontryagin's principle	Block teaching (4 hr)
Week 11	Stochastic differential games	Block teaching (4 hr)
Week 12	Nonlinear Feynman-Kac theorem	Block teaching (4 hr)
Week 13	Nonlinear Markovian financial models	Block teaching (4 hr)

Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Required readings

Course notes provided.

Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

Outcomes
Graduate qualities

At the completion of this unit, you should be able to:

LO1. Demonstrate familiarity with fundamental concepts in the general theory of stochastic processes.
LO2. Understand the concept of a backward stochastic differential equation and the proof of the main existence and uniqueness of solutions theorem.
LO3. Understand the comparison property for solutions to a BSDE and its applications to other stochastic problems.
LO4. Be capable of analysing optimal stopping problems using a reflected BSDE.
LO5. Analyse two-person stochastic Dynkin games using a doubly reflected BSDE.
LO6. Analyse and solve optimal control problems via the Hamilton-Jacobi-Bellman equation.
LO7. Analyse optimal control problems via the stochastic Pontryagin principle.
LO8. Analyse stochastic differential games and identify its value process.
LO9. Analyse and apply the Feynman–Kac formula for solutions to quasi-linear parabolic PDEs.

Graduate qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1	Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.
GQ2	Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.
GQ3	Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.
GQ4	Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.
GQ5	Inventiveness Generating novel ideas and solutions.
GQ6	Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.
GQ7	Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.
GQ8	Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.
GQ9	Influence Engaging others in a process, idea or vision.

Outcome map

Learning outcomes	Graduate qualities
Learning outcomes

Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

Some changes have been made since this unit was last offered.

Disclaimer

The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

To help you understand common terms that we use at the University, we offer an online glossary.

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Study commitment

Required readings

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Disclaimer

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