Syllabus academic year 2009/2010
(Created 2009-08-11.)
COMPLEX ECONOMYFMF170

Higher education credits: 7,5. Grading scale: TH. Level: G2 (First level). Language of instruction: The course will be given in English. Optional for: F3, F3sfm, I4, Pi4, Pi4fm. Course coordinator: Professor Sven Ă…berg, sven.aberg@matfys.lth.se, Fysik, kurslaboratoriet. Recommended prerequisits: Basic calculus, linear algebra and fourier transforms. Assessment: The exam is written, the students work on problems which require calculations and to a lesser extent description and explanation. This exam determines the grade/mark. Home page: http://www.matfys.lth.se/complexeconomy.html.

Aim
Why do banks and consulting firms hire an ever larger number of physicists? - Because the methods of statistical physics are becoming more and more important in economics. This course is an introduction to this quickly expanding field. The emphasis will be on the understanding of concepts and ideas and their universal applicability.
The course aims at giving, first, insight into the general merit that methods from statistical physics and chaos theory have in the economical sciences, second, the ability to critically evaluate the potential and the limits of scientific transfer and, third, an intuition for the large impact that quantitative methods can have in a fast developing interdisciplinary field.

Knowledge and understanding
For a passing grade the student must

Skills and abilities
For a passing grade the student must

Judgement and approach
For a passing grade the student must

Contents
Some introductory remarks about statistical physics

Basic concepts and mechanisms in the economy and in the capital markets: arbitrage, stocks, financial derivatives, options, portfolio, risk management

Statistical models for stock markets: classes of Brownian motion, stochastic processes, probabilities and distributions, limit theorems, physics interpretation

Black and Scholes theory for options: diffusion equations, Ito?s lemma, quantitative risk management, hedging

Correlations between stocks: impact on risk management, random matrices, formal similarities to quantum chaotic systems in physics

Controversial and speculative theories: Can one predict market crashes? Are there similarities between market crashes and earth quakes?

Literature
Guhr, T: Econophysics (lecture notes), Lund 2005