Matematisk Fysik

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The Course is given January-March 2016

(The course will NOT be given in 2017)

Why do banks, consulting firms and insurance companies hire more and more physicists? - Because the methods from statistical physics become increasingly important to model economical systems and, in particular, the capital markets. This course is an introduction to this quickly expanding field. It is often called Complex Economy or Econophysics.

The floor

This is how "the floor" looks when something truly exciting happens.
The floor is the place in the stock exchange where the brokers meet and do the trading.

The stocks of companies are traded at stock exchanges. The people who do that professionally are called stock brokers. They buy or sell specific stocks because they expect them to go up or down in value. Thus, they have a certain market expectation. However, it is known that the value of a stock, as you see it in the chart below, can be modeled by a stochastic process. This does not mean that there is no ``deterministic'' reason for the value to change. It is very much like the motion of an oxygen molecule in the air: its motion is not random, but it can be modeled as a random process. Such considerations make it possible to apply the powerful machinery of statistical physics in the capital markets. For example, the Black and Scholes theory yields quantitative predictions for the values of financial derivatives, such as options.

This is a chart. It shows the value of a stock for a given company as a function of time. Here, the company is NOKIA, and you see its performance from end of May 2000 to end of May 2001 at the Stockholm stock exchange.

If you feel like looking at more charts like this one of stocks, options, indices, exchange rates, etc., comdirect provides a very useful service.

Nokia stock from end of
                    May 2000 to end of May 2001

In this course, you will not learn how to get rich quickly. You will learn solid tools of statistical physics and how they are applied to the economy. However, because the field is so new, we will also discuss a few speculative models. You do not need a background in economics! - In the course, you will learn the basics that we need. The course is suitable for everybody who has a sufficient background in mathematics, as it is taught in the basic courses for physicists. Physics background is helpful, but not required. Thus, the course is also suitable for non-physicists.

A note in Nature (2008) on "Economics needs a scientific revolution" by JP Bouchaud.


Content of the course

  • 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?


The reference number of the course (kurskod) is FMF170. Syllabus

The course is given in English.


are given Tuesdays and Thursdays 13.15-15.00
in lecture room F (Fys:K404), Physics Dept.
The course starts on Tuesday, 21th of January 2014 at 13.15.


are offered Wendesdays 8.15-10.00 in seminar room Fys:K262, Sölvegatan 14A.
On Wednesday 9th March 08.15-10.00 solutions to the exam given March 2014 will be discussed.
This will taker place in lecture room F (Fys:K404).

Preliminary plan for the lectures

Lecture Time Part in compendium
1 19/1 13-15 Ch 1,2: Some Remarks about Statistical Physics. Some Basic Concepts
2 21/1 13-15 Ch 2: Basic Concepts in the Economy and in the Capital Market
3 26/1 13-15 Ch 2,3: Statistical Modelling
4 28/1 13-15 Ch 3
5 2/2 13-15 Ch 3
6 4/2 13-15 Ch 3
7 9/2 13-15 Ch 3
8 11/2 13-15 Ch 3,4: Black and Scholes Theory for Options
9 16/2 13-15 Ch 4
10 18/2 13-15 Ch 4
11 1/3 13-15 Ch 4
12 3/3 13-15 Ch 5: Correlations between Stocks
13 8/3 13-15 Ch 5
14 10/3 13-15 Ch 5,6:: Earthquakes and Market Crashes



Lectures and responsible for the course: professor Sven Åberg
Exercises: Daniel Ward


Written examination, Wednesday March 16th, 8.00-13.00, Sparta:B, Sparta:C


Complex Economy, Thomas Guhr, Compendium (2007), Mathematical Physics, Lund.
The compendium is sold at the first lecture (price: 150 SEK), and after that by Katarina Lindqvist, Mathematical Physics

For more information, send e-mail to or call 046 222 9633, Matematisk Fysik, Professorsgatan 1, Lund.