From a statistical mechanics point of view I investigate both production and transmission of information in complex systems which consist of many interacting elements. Despite simplicity of elements the systems often behave in incredibly complicated way. We can find such systems, which are called complex systems, in economics, sociology, biology, physics, such as financial markets, human groups, traffic flows, organs, cells, fluid dynamics turbulence, and so on. For example in economics a company consists of many individuals, and the companies are related to one another. In financial markets participants communicate with one another through market places or brokerage systems. In biology, organs consist of many cells, the organs are related to one another and organisms consist of several organs. The Internet is one of the most familiar examples in the information transmission. Small LAN (Local Area Network) contains several computers, and WAN (Wide Area Network) consists of several small LANs. Information is transmitted via computers.
The objectives of my studies are both to mathematically clarify common mechanisms of many interacting elements and to develop methodology for designing them. In the world we know that there are many synergy phenomena (collective behaviors) of many interacting elements. The collective behavior is both the inter-disciplinary and fundamental key-concept in various systems. For example,
- Laser: interaction between atoms and phonon,
- Internet: interaction between computers connected to the Internet,
- Socio-economic phenomena: interaction between individuals through human communication,
- Brain: chemical and electronic interplay between many neuronal cells.
Especially we can expect that if one can deeply understand universal mechanism of the synergy phenomenon, then one may control and design a system consisting of many interacting elements. In fact several people may be critical of my expectation because of over-simplification and over-optimism, however, there are several forerunners who have tried and succeed. For example, in 1940s complex systems and self-organization have been discussed in cybernetics, in 1980s macroscopic properties of complex systems have been approached in Haken's synergetics.
Recently I focus on socio-economic phenomena from a statistical physics point of view. Such a movement called socio-econophysics, which has been established since 1997 and is a novel branch in statistical mechanics. Main research targets in econophysics are financial market, wealth distributions of both companies and individuals, money flow and products' flow, large scale network analysis of relationship among agents (individuals) and super agents (companies). Specifically I have interests in financial markets based on behavioral similarities among market participants and price fluctuations.
Why, how, when, and where market prices fluctuate? Motivated by these questions we develop agent-based models of a financial market in which many market participants exchange several kinds of financial commodities, and examine stochastic description of behavior of financial markets from a mesoscopic point of view. This study is conducted with the intention of bridging a gap between microscopic agent-based approach and macroscopic statistics of several properties observed in economics. Description of stochastic processes is a useful methodology to investigate complex systems from mesoscopic point of view. Our current research interests are as follows:
Motivated by statistical mechanics data-centric studies on socio-economic systems are of remarkable interests in both physics and economics. Such kinds of collaborations are called econophysics and/or sociophysics. Several collaborative works between economists/sociologist and physicists have been done all over the world.
From the end of 1990s our society started to be computerized from information processing to communication due to both development and spread of the Information and Communication Technology (ICT). Consequently it allows us to accumulate data on human activity and to directly analyze them by means of both mathematical physics and computer sciences. During this period seeds of both mathematical physics and computer sciences and needs of understanding of human activity met together. In my opinion advent of socio-econophysics at that moment seems not to be in chance and to be in necessity.
Foreign exchange market
The foreign exchange market is the largest financial market all over the world. The foreign exchange market is not organized at a market place but is a network consisting of bank traders, brokers, and electronic equipments. Currently both development and spread of Information and Communication technology enable us to accumulate data on the foreign exchange market and to investigate states of the foreign exchange market based on the large amounts of data. Ultra-high frequency data and high-resolution data will provide us insights on world economy from a holistic point of view.
Specifically I focus on both quotation and transaction activities of market participants and quantify states of the foreign exchange market by means of mathematical tools with a large amount of high-resolution data in a parallel computer system consisting of several high performance computers. I am expecting that it will be able to quantify and visualize the foreign exchange market from comprehensive point of view.
Fluctuation scaling of the foreign exchange market
The fluctuation scaling is referred as to a scaling relationship between temporal means of the number of arrival at a node and their standard deviations. The fluctuation scaling is found in wide spectrum of fields such as physics, finance, biology, sociology and so on. In the case of independent Poissonian random variables the scaling index can be theoretically calculated as 1/2. In the case of random coefficients times a Poissonian random variable it can be described as 1.
We computed the number of incoming quotations and occurrence of transactions for each currency pairs at an electronic brokerage system and showed that there exists scaling relationship between temporal means of the number of quotations and transactions and their standard deviations. Furthermore it is found that the scaling indices depend on degrees of synchronization of participants activities in the foreign exchange market.
Stochastic resonance in the foreign exchange market
I found periodic motions of quotation frequencies in the foreign exchange market by analyzing the quotation frequencies extracted from the high-frequency financial data with spectral methods. In these analyzes I found several peaks in the power spectra at high frequency regime (from 2 to 5 minutes). Moreover the peak height varies depending on observation periods. In order to explain this finding I both theoretically and numerically analyzed the agent-based model where N market participants who perceive periodical exogenous signals exchange M financial assets and propose a hypothesis that stochastic resonance occurs in the foreign exchange market. If this hypothesis is correct then the signal-to-noise ratio calculated from the peak height is related to uncertainty of market participant's interpretation of information. Furthermore relationship among the characteristic frequencies may be related to a special group structure among market participants.
In order to check adequateness of the mathematical tools to quantify states of financial markets I am developing a mathematical model of financial markets based on agent-based modeling. Developing model is of a agent model in which N market participants trade M financial assets. Stylized facts can be reproduced by this agent-based model. As a result of numerical simulations it was found a distribution of behavioral parameters of market participants is related to states of financial markets.
The Java applet simulator of an artificial market where N market participants trade a kind of commodity is available. [Java applet]
The power spectrum calculated from quotation frequencies of USD/JPY for a period from 1st to 31st April 2001. We can find several peaks in this power spectrum.
Recently E-commerce systems are popular places to purchase and to exchange goods and services, and are used by a lot of persons. Usually E-commerce systems are constructed by data base servers and web servers. In the data base servers data on quotations and transactions of goods and services are inserted and deleted by many customers and retailers in time. If we extract cross sectional data from E-commerce systems and accumulate them, then we will be able to obtain insights on socio-economic tendency and/or utilities. I am developing a platform to collect data and methodologies to quantify and visualize states of economic activities from a holistic point of view.