Instructor: Péter Érdi, Henry R. Luce Professor
Office: OU 208/B. Email: perdi@kzoo.edu
Goal:
The goal is to explain why and how concepts and methods of physics has
influenced the development of economics. While classical theories of economics
study mostly equilibrium behaviors, dynamical models of mathematical physics
contribute to understanding the dynamics of economical behavior.
In the first half of the course you will learn typical non-equilibrium,
nonlinear phenomena, as economical cycles and chaotic phenomena. In the second
half of the term probabilistic methods
will be presented to study large fluctuations, extreme events. This second area
belongs narrowly speaking a new field, called econophysics.
The websites of Econophysics Forum is:
http://www.unifr.ch/econophysics/
Course structure:
Ten topics will be discussed. We shall spend one week on each topic.
During the term it will be possible to make reports on readings.
Exam: There will be a sixty minutes long written midterm and an
essay type final.
Topics:
1. Physics and Economics: Historical Aspects
www.ge.infm.it/econophysics/tutorial/savona1.ps
Theoretical frameworks versus statistical data analysis
A non-equilibrium and nonlinear dynamical economics
Statistical physical approach
Bounded rationality
Large fluctuation
2. Basic Dynamic Phenomena
Boundless growth: linear, exponential, super-exponential growth
Growth to equilibrium
Boom-and-bust
Multistability
Oscillation and chaos
3. Business Cycles and Multistability
Kaldor model. Kaldor-Kalezki model.
http://cepa.newschool.edu/~het/essays/multacc/kaldcyc.htm
On nonlinear mechanics of business cycle model.
Regular and Chaotic Dynamics 6(101-118)2001
A catastrophe theoretical model of oil price changes
http://www.kkrva.se/Artiklar/003/woodcock.html
http://www.gold-eagle.com/editorials_02/douglasa061302.html
4. Chaos and Chaos Control in Economics
Chaos theory: basic models.
M Christen, Th Ott, A Kern, N Stoop and R Stoop
Periodic economic cycles: the effect of evolution towards criticality,
and control
http://www.iop.org/EJ/article/1742-5468/2005/11/P11013/jstat5_11_p11013.html
J.A. Hoyst and K. Urbanowicz:
Chaos control in economical model by time-delayed feedback method
Physica A, 287, 587-598 (2000)
to be downloaded from: http://www.if.pw.edu.pl/~jholyst/econom.htm
5. Elements of Probability Theory and of Stochastic
Processes
Basic probability theory, Gaussian distributions. Examples for
deviations from Gaussian distributions. Pareto distribution.
Stochastic processes. Brownian motion: its role in physics and
economics. Fokker Planck equation. Stochastic differential equations.
Extreme value theory.
http://mahalanobis.twoday.net/stories/210704/
Distribution fittings
http://www.statsoft.com/textbook/stdisfit.html
6. Stock Market Crashes: Examples and Elementary
Analysis
http://www.stock-market-crash.net/
7. Dynamical Models of
Stock Market Crashes: Self-organized Criticality versus Intermittent
Criticality
The sandpile model
http://web.pdx.edu/~rueterj/courses/viewers/patterns/sandpile.html
http://www.tn.tudelft.nl/tn/People/Staff/Thijssen/sandexpl.html
Finite time singularities
8. Dynamics of Speculative Peaks
Collective behavior of investors. Shape of price peaks: mathematical
description. Exponential and super-exponential growth: there is a difference.
Background: Roehner BM: Patterns of Speculation. Cambridge Univ. Press,
2002.
9. Option Pricing theory: a success story
http://www.riskglossary.com/link/option_pricing_theory.htm
The Black-Scholes model
http://bradley.bradley.edu/~arr/bsm/model.html
10. Where we are now?
Student reports about readings.