(Created 2009-08-11.)

COMPLEX ECONOMY | FMF170 |

**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 expandingÂ 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

- know certain basic mechanisms in the economy and important statistical models that are applied in studying the capital markets
- know the Black and Scholes theory for options, effects due to financial correlations and the concepts of portfolio and risk management

*Skills and abilities*

For a passing grade the student must

- be able to carry out simple statistical analyses, calculate option prices and measure financial correlations
- apply principles of risk management
- have developed an ability to analyse economical problems with mathematical methods

*Judgement and approach*

For a passing grade the student must

- be able to describe and discuss some of the most important concepts in the interdisciplinary field econophysics/complex economy
- be able to explain basic theoretical and mathematical concepts that are needed in economocal risk management
- understand not too advanced scientific articles about risk managment in the context of physical and statistical methods in economics
- apply information from other sources to solve new problems

**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