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Unit of study_

MATH2070: Optimisation and Financial Mathematics

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.

Details

Academic unit Mathematics and Statistics Academic Operations
Unit code MATH2070
Unit name Optimisation and Financial Mathematics
Session, year
? 
Semester 2, 2021
Attendance mode Normal day
Location Camperdown/Darlington, Sydney
Credit points 6

Enrolment rules

Prohibitions
? 
MATH2010 or MATH2033 or MATH2933 or MATH2970 or ECMT3510
Prerequisites
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(MATH1X21 or MATH1011 or MATH1931 or MATH1X01 or MATH1906) and (MATH1014 or MATH1X02)
Corequisites
? 
None
Assumed knowledge
? 

MATH1X23 or MATH1933 or MATH1X03 or MATH1907

Available to study abroad and exchange students

Yes

Teaching staff and contact details

Coordinator Jie Fan, jieyen.fan@sydney.edu.au
Type Description Weight Due Length
Final exam (Record+) Type B final exam Final exam
Examination
70% Formal exam period 2 hours
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6
Assignment Assignment
Assignment
10% Week 07
Due date: 20 Sep 2021
2 weeks
Outcomes assessed: LO1 LO2 LO3 LO6
Small test Quiz
Quiz
5% Week 11
Due date: 25 Oct 2021
40 minutes
Outcomes assessed: LO1 LO6 LO5 LO4 LO3 LO2
Assignment Computer project
Project
15% Week 12
Due date: 05 Nov 2021
3 weeks
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6
Type B final exam = Type B final exam ?

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.

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.

Special consideration

If you experience short-term circumstances beyond your control, such as illness, injury or misadventure or if you have essential commitments which impact your preparation or performance in an assessment, you may be eligible for special consideration or special arrangements.

Academic integrity

The Current Student website provides information on academic honesty, academic dishonesty, 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 dishonesty or plagiarism seriously.

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

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

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

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

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