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Unit of study_
MATH2070: Optimisation and Financial Mathematics
2025 unit information
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 and the Capital Asset Pricing Model. 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
Managing faculty or University school:
Science
| Study level | Undergraduate |
|---|---|
| Academic unit | Mathematics and Statistics Academic Operations |
| Credit points | 6 |
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Prerequisites:
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{(MATH1X61 or MATH1971) or [(MATH1X21 or MATH1011 or MATH1931 or MATH1X01 or MATH1906) and (MATH1014 or MATH1X02)]} and (MATH1X62 or MATH1972 or MATH1X23 or MATH1933) |
|---|---|
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Corequisites:
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None |
| Prohibitions:
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MATH2970 |
| Assumed knowledge:
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Multivariable calculus such as MATH1X23 or MATH1X62 |
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.
Unit availability
This section lists the session, attendance modes and locations the unit is available in. There is a unit outline for each of the unit availabilities, which gives you information about the unit including assessment details and a schedule of weekly activities.
The outline is published 2 weeks before the first day of teaching. You can look at previous outlines for a guide to the details of a unit.
| Session | MoA ? | Location | Outline ? |
|---|---|---|---|
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Semester 2 2025
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Normal day | Camperdown/Darlington, Sydney |
Outline unavailable
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Modes of attendance (MoA)
This refers to the Mode of attendance (MoA) for the unit as it appears when you’re selecting your units in Sydney Student. Find more information about modes of attendance on our website.
Important enrolment information
Additional advice
Students may enrol in both MATH2070 and MATH3075 in the same semester
