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).

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. 4 hours of lectures and 2 hours of seminars in the ST.

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 main exam period.