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Unit of study_

MATH2070: Optimisation and Financial Mathematics

Overview

Problems in industry and commerce often involve maximising profits or minimising costs subject to constraints arising from resource limitations. The first part of this unit looks at programming problems and their solution using the simplex algorithm; nonlinear optimisation and the Kuhn Tucker conditions. The second part of the unit deals with utility theory and modern portfolio theory. Topics covered include: pricing under the principles of expected return and expected utility; mean-variance Markowitz portfolio theory, the Capital Asset Pricing Model, log-optimal portfolios and the Kelly criterion; dynamical programming. Some understanding of probability theory including distributions and expectations is required in this part. Theory developed in lectures will be complemented by computer laboratory sessions using Python. Minimal computing experience will be required.

Unit details and rules

Unit code MATH2070 Mathematics and Statistics Academic Operations 6 MATH2010 or MATH2033 or MATH2933 or MATH2970 or ECMT3510 (MATH1X21 or MATH1011 or MATH1931 or MATH1X01 or MATH1906) and (MATH1014 or MATH1X02) None MATH1X23 or MATH1933 or MATH1X03 or MATH1907 Yes

Teaching staff

Coordinator Jie Yen Yen Fan, jieyen.fan@sydney.edu.au

Assessment

Type Description Weight Due Length
Final exam (Record+) Final exam
Examination
70% Formal exam period 2 hours
Outcomes assessed:
Assignment Assignment
Assignment
10% Week 07
Due date: 20 Sep 2021 at 23:59
2 weeks
Outcomes assessed:
Small test Quiz
Quiz
5% Week 11
Due date: 25 Oct 2021 at 10:00
40 minutes
Outcomes assessed:
Assignment Computer project
Project
15% Week 12
Due date: 05 Nov 2021 at 23:59
3 weeks
Outcomes assessed:
= Type B final exam

Assessment summary

Detailed information for each assessment can be found on Canvas

Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

For more information see sydney.edu.au/students/guide-to-grades.

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.

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.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

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.

Weekly schedule

WK Topic Learning activity Learning outcomes
Week 01 1. Introduction; 2. Introduction to optimisation and linear programming Lecture (3 hr)
Week 02 1. Graphical solution to LP problems; 2. Simplex algorithm Lecture (3 hr)
Week 03 Non-standard LP problems and two-phase simplex algorithm Lecture (3 hr)
Week 04 1. Non-standard LP problems; 2. Duality Lecture (3 hr)
Week 05 Nonlinear optimisation without constraints Lecture (3 hr)
Week 06 Nonlinear optimisation with constraints Lecture (3 hr)
Week 07 Probability review Lecture (3 hr)
Week 08 1. Decision under uncertainty; 2. Utility theory Lecture (3 hr)
Week 09 1. Utility theory; 2. Portfolio basics Lecture (3 hr)
Week 10 Portfolio theory: portfolio selection rules and 2-asset portfolios Lecture (3 hr)
Week 11 Portfolio theory: unrestricted n-asset portfolios Lecture (3 hr)
Week 12 1. Portfolio theory: restricted n-asset portfolios; 2. Capital asset pricing model Lecture (3 hr)
Weekly Problems linked with lectures with one week lag Tutorial (1 hr)
Computer problems linked with lectures with one week lag Computer laboratory (1 hr)

Attendance and class requirements

• Unless otherwise indicated, students are expected to attend a minimum of 80% of timetabled activities for a unit of study, unless granted exemption by the Associate Dean.
• For some units of study the minimum attendance requirement, as specified in the relevant table of units or the unit of study outline, may be greater than 80%. The Associate Dean may determine that a student has failed a unit of study because of inadequate attendance. Further details are available from the Science Undergraduate Handbook 2019: https://sydney.edu.au/handbooks/science/coursework/faculty_resolutions and the Science Postgraduate Handbook 2019: https://sydney.edu.au/handbooks/science_PG/

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.

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.

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

• LO1. demonstrate familiarity with the concepts in linear programming (standard and non-standard) and simplex algorithm, and apply them to solve concrete problems
• LO2. demonstrate familiarity with the concepts in non-linear optimisation without constraints. Explain how the rule based on Hessian can be used to determine minima and maxima, and apply it to solve concrete problems
• LO3. demonstrate familiarity with the concepts in non-linear optimisation with constraints, and apply suitable methods (Lagrange multipliers and KKT conditions) to solve concrete problems
• LO4. demonstrate understanding of the notions from utility theory and explain the difference between principles of expected return and expected utility. Apply this knowledge to solve practical problems
• LO5. demonstrate a coherent and advanced knowledge of the fundamental concepts in portfolio theory and capital asset pricing model
• LO6. identify, formulate and solve original practical problems that can be addressed using mathematical and computational techniques you learned in this unit.

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
GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

Responding to student feedback

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

No changes have been made since this unit was last offered.

Additional information

Work, health and safety

We are governed by the Work Health and Safety Act 2011, Work Health and Safety Regulation 2011 and Codes of Practice. Penalties for non-compliance have increased. Everyone has a responsibility for health and safety at work. The University’s Work Health and Safety policy explains the responsibilities and expectations of workers and others, and the procedures for managing WHS risks associated with University activities.

General Laboratory Safety Rules

• No eating or drinking is allowed in any laboratory under any circumstances

• A laboratory coat and closed-toe shoes are mandatory

• Follow safety instructions in your manual and posted in laboratories

• In case of fire, follow instructions posted outside the laboratory door

• First aid kits, eye wash and fire extinguishers are located in or immediately outside each laboratory

• As a precautionary measure, it is recommended that you have a current tetanus immunisation. This can be obtained from University Health Service: unihealth.usyd.edu.au/

Disclaimer

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