What is white, pink, "brown" and even black? It is around us every day and usually is very useful. Yet from time to time it annoys us and sometimes we even call police to keep it in check? The answer to this quite complex, as it is oriented towards people with physics background, question is unbelievably simple. Noise possesses all of the aforementioned qualities!
Considerable part of stochastic models available on Physics of Risk website (ex., Agent based herding model of financial markets or Long-range memory stochastic model of return) are related to the general class of stochastic differential equations derived by our group [1, 2]. The general form of this class is the following stochastic differential equation:
\begin{equation} \mathrm{d} x = \left(\eta - \frac{\lambda}{2} \right)x^{2 \eta -1} \mathrm{d} t + x^\eta \mathrm{d} W . \label{sde} \end{equation}
In our talks at various scientific events and on Physics of Risk itself we frequently say that this equation also encompasses other widely known stochastic processes. Thus further in this text we will show some of the relations between this class and some widely known stochastic processes.
EURO 2012 starts next week in Vilnius! EURO 2012, European Conference on Operational Research, is huge scientific event popular both among scientists and businessmen. Operational research tackles very challenging, and thus scientifically interesting, and highly applicable topics. Some of these topics overlap with the ones we discuss here on Physics of Risk - financial market modeling, risk management and analysis, decision making. Many reports will also consider logistics, optimization and network analysis.
On of our authors will join numerous scientists from Lithuania and abroad giving talks in the conference. On Monday, the 9th of July, he will give a talk on "Herding behavior of agents as a background of financial fluctuations", Our works on the applications of Kirman model will be the key point of the talk.
It should be pretty straightforward why the agent-based models appear to be very simple. They do poses technical simplicity, which my cause some doubts on the actual usefulness of the agent-based models. But the fact is that they are able to reproduce complex, non-trivial behavioral patterns.
Traditionally it is thought that economics and physics are very different irreconcilable sciences. Physicists sometimes claim that economists are aware only of addition and subtraction, while only very rarely they attempt to use multiplication or even division. Economists on the other hand think that physicists are busy dividing molecules into atoms, create atomic weapons and lasers and are able to fix AC sockets, while having absolutely no understanding in other, nontechnical, fields. Evidently this oversimplified thinking is incorrect - economics and physics have things in many common. And with the time more common things are discovered.
What is common between physics, a precise science about inanimate nature, and economics, a social science considering human interactions in certain scenarios? While it might sound a bit strange at first, but some of the processes in both sciences are very similar! Thus physicists can successfully apply their knowledge and experience to understand, describe, model and forecast various processes in economics. Econophysics is a cognitive science, which attempts to see the reasons behind various economic processes. Physicists are always obsessed with simple equation - why?
These are free translations of the texts published in "Science and life" (lt. "Mokslas ir gyvenimas") journal by prof. Kęstutis Staliūnas [1, 2]. These are few rare texts about econophysics published in Lithuanian language.
Another interesting text is an electronic course material [3] written for the students of Physics Faculty of Vilnius University (the econophysics course was taught there in 2002-2003). This contains broader review of introductory topics to econophysics.
Physics of risk, complexity and socio-economic systems.