Not available in 2021/22
MA418      Half Unit
Preferences, Optimal Portfolio Choice, and Equilibrium

This information is for the 2021/22 session.

Teacher responsible

Dr Albina Danilova


This course is available on the MSc in Applicable Mathematics and MSc in Financial Mathematics. This course is available with permission as an outside option to students on other programmes where regulations permit.


Students must have completed either Stochastic Processes (ST409) or Probability and Measure (MA411) or The Mathematics of the Black and Scholes Theory (MA415).

Course content

This course is concerned with the theory of optimal investment and consumption. The course starts with the derivation of utility functions from the axioms of an agent's preferences. Utility functions are then used as a measure of portfolio performance in a financial market. Optimal investment and consumption strategies are obtained for various utility functions in both complete and some types of incomplete markets. Equilibrium and asset price formation are considered in the context of complete and informationally incomplete markets


20 hours of lectures and 10 hours of seminars in the LT.

Indicative reading

R.A.Dana and M.Jeanblanc, Financial Markets in Continuous Time; Springer; I D.Duffie, Dynamic Asset Pricing, Princeton University Press; I.Karatzas and S.E.Shreve, Methods of Mathematical Finance, Springer.


Exam (100%, duration: 3 hours) in the summer exam period.

Course selection videos

Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.

Important information in response to COVID-19

Please note that during 2021/22 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the differing needs of students in attendance on campus and those who might be studying online. For example, this may involve changes to the mode of teaching delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.

Key facts

Department: Mathematics

Total students 2020/21: Unavailable

Average class size 2020/21: Unavailable

Controlled access 2020/21: No

Value: Half Unit

Guidelines for interpreting course guide information

Personal development skills

  • Self-management
  • Problem solving
  • Application of information skills
  • Communication
  • Application of numeracy skills
  • Specialist skills