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:  Every Thursday 10.00-12.00. First lecture: Thursday, 11th of January.
Location: Clement House, CLM 3.02
Remark:There are also weekly exercise sessions starting from Week 2. They will be held in Old Building in room OLD2.22 on Wednesdays 12-13.

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

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


Course summary:

Indicative reading:
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

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.

Merton's optimal investment problem; utility maximisation by duality methods; incomplete markets and indifference pricing; techniques - dynamic programming, convex duality, viscosity solutions. 
MF0 Stochastic integrals: an introduction to the Itō calculus

Lecturer: Dr. Eyal Neuman, Imperial
Time and dates: Spring Semester, Mondays 4-7 pm ( the exact dates to be confirmed)
Location:Lectures will take place at Imperial College, the room will be announced later. 

Knowledge of measure theory, probability theory and martingales is assumed as a prerequisite.

Course summary:
This course is an introduction to the Ito calculus, a calculus applicable to functions of stochastic processes with irregular paths, which has many applications in finance, engineering and physics. The course shall focus on the mathematical foundations of stochastic calculus and the theory of stochastic integration, using a less conventional approach which emphasizes pathwise, rather than probabilistic, methods.
The first part of the course will focus on pathwise integration with respect to functions of finite quadratic variation, without using any probabilistic tools.
The second part of the course will explore the application of these results to stochastic integrations with respect to semimartingales, a setting which covers most examples of stochastic processes of interest in applications - including jump processes and diffusion processes. 

Indicative reading:
Stochastic Integration and Differential Equations, by Philip E. Protter
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