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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.

Code MATH2070
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
(MATH1X21 or MATH1011 or MATH1931 or MATH1X01 or MATH1906) and (MATH1014 or MATH1X02)
MATH2010 or MATH2033 or MATH2933 or MATH2970 or ECMT3510
Assumed knowledge:
MATH1X23 or MATH1933 or MATH1X03 or MATH1907

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 outlines

Unit outlines will be available 2 weeks before the first day of teaching for the relevant session.