MF4 Portfolio Optimisation
Lecturer: Dr. Albina Danilova, LSE
Time and dates: Mondays, 18.00 – 21.00 (8th January – first lecture, 12th March – last lecture)
Students must have completed a course on martingales in continuous time, Brownian motion, and Ito calculus.
This course is concerned with the optimal consumption and investment under given agent's preferences.
The course will start from an overview of utility functions, and their relationship to the axioms of (agent’s) choice. They then will be used as a measure of portfolio performance on a financial market.
Optimal investment and consumption will be obtained for various utility functions for both complete and (some types of) incomplete markets. Methods that will be used will include stochastic control and duality theory. In the context of stochastic control we will discuss dynamic programming principle and verification results in classical and viscosity formulations.
Finally, derivative pricing via utility indifference will be discussed for both complete and informationally incomplete markets.
Merton's optimal investment problem; utility maximisation by duality methods; incomplete markets and indifference pricing; techniques - dynamic programming, convex duality, viscosity solutions.