Courses offered in Jan-Mar 2018

Courses offered 
in Jan-Mar 2018
MF9 Introduction to Markov Process and their Applications

Lecturer: Dr. Umut Cetin, LSE
Time and dates: TBC
Location: TBC

Prerequisites: 
Students must have completed a course on martingales in continuous time, Brownian motion, and Ito calculus. 

Course summary:
Markov property and transition functions. Feller processes. Strong Markov property. Martingale problem and stochastic differential equations, relation with partial differential equations. 
Diffusion processes. One dimensional diffusions. Selection of topics from filtering of diffusion processes. Applications
MF12 Incomplete Markets

Lecturer: Dr. Teemu Pennanen, King's College
Time and dates: at 11.00-13.00 on 12/01/18, 19/01/18, 26/01/18, 02/02/18, 09/02/18, 16/02/18, 23/02/18, 02/03/18, 09/03/18, 16/03/18, 23/03/18
Location: STRAND BLDG S-1.27, King's College London

Objectives: 
This module aims to give students an understanding of the main issues in the valuation and hedging of financial products in incomplete markets and to give them an introduction to convex analysis relevant in mathematical analysis of such problems.

Course summary:
Optimal investment and valuation of contingent claims in incomplete financial markets with transaction costs, illiquidity effects and portfolio constraints. Basic properties of convex sets and functions. Convex duality, martingale measures, state-price densities and model calibration will also be discussed.
MF25 Commodities Derivatives

Lecturer: Dr. Helyette Geman, Birkbeck
Time and dates: TBC
Location: TBC

Prerequisites: 
TBC

Course summary:
TBC

Indicative reading:
TBC
MF4 Portfolio Optimisation

Lecturer: Dr. Albina Danilova, LSE
Time and dates: Mondays, 18.00 – 21.00 (8th January – first lecture, 12th March – last lecture)
Location:KSW.1.04, LSE

Prerequisites: 
Students must have completed a course on martingales in continuous time, Brownian motion, and Ito calculus. 

Course summary:
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.

Keywords:
Merton's optimal investment problem; utility maximisation by duality methods; incomplete markets and indifference pricing; techniques - dynamic programming, convex duality, viscosity solutions. 
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