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We describe a new financial diagnostic method, related to the entropy generated when a limit trader satisfies market demand by filling orders, thereby playing the role of a Maxwell Demon. By comparing the real cumulative trading volume to some measure of historically “normal” demand, one may determine whether the market shows excess order or disorder, and accordingly adjust one’s trading strategy.

We examined the effectiveness of random matrix theory applied to portfolio optimization using Japanese stock market data. We carried out 48 back tests for different historical periods and confirmed that it was possible to drastically improve the accuracy of portfolio risk evaluation using random matrix theory.

Small-business firms have qualitatively different characteristics of firm-size growth from those for large firms. Credit Risk Database (CRD) is the largest database of japanese small and midsize companies, which covers nearly 1 million small-business firms, more than 60% of all companies in Japan. By employing stock (total assets and debts) and flow (sales) quantities in the CRD, we show that Gibrat’s law breaks down for the small and midsize companies corresponding to non-power-law region, while the law asymptotically holds in the larger-size region, for all the variables examined. In fact, standard deviation of logarithmic growth rate = log = log(/) (where and are the variable for two successive years) scales as firm size becomes larger ()), but asymptotically approaches non-scaling regime ( ∼ const). We also show that there is scaling relation of growth rates for different time-scales with which one observes firm-size. Standard deviation of growth rate = log = log(/) from time and + scales as ().

A so called Zipf analysis portofolio management technique is introduced in order to comprehend the risk and returns. Two portofoios are built each from a well known financial index. The portofolio management is based on two approaches: one called the “equally weighted portofolio”, the other the “confidence parametrized portofolio”. A discussion of the (yearly) expected return, variance, Sharpe ratio and follows. Optimization levels of high returns or low risks are found.

Economic flows are modeled based on the microscopic particle pictures, and studied by renormalized stochastic dynamics and simulations. From the universal behavior obtained, every catastrophic behavior of the flows may be understood, as well as which sub-system is concerned and how to avoid it by suitable control measures.

As complex networks in economics, we consider Japanese shareholding networks as they existed in 1985, 1990, 1995, 2000, 2002, and 2003. In this study, we use as data lists of shareholders for companies listed on the stock market or on the over-the-counter market. The lengths of the shareholder lists vary with the companies, and we use lists for the top 20 shareholders. We represent these shareholding networks as a directed graph by drawing arrows from shareholders to stock corporations. Consequently, the distribution of incoming edges has an upper bound, while that of outgoing edges has no bound. This representation shows that for all years the distributions of outgoing degrees can be well explained by the power law function with an exponential tail. The exponent depends on the year and the country, while the power law shape is maintained universally. We show that the exponent strongly correlates with the long-term shareholding rate and the cross-shareholding rate.

We describe a new financial diagnostic method, related to the entropy generated when a limit trader satisfies market demand by filling orders, thereby playing the role of a Maxwell Demon. By comparing the real cumulative trading volume to some measure of historically “normal” demand, one may determine whether the market shows excess order or disorder, and accordingly adjust one’s trading strategy.

The impacts of money creation on the statistical mechanics of money circulation were investigated by focusing on the dependence of monetary wealth distribution and the velocity of money on the required reserve ratio in this paper. In reality, money creation is important to economic system. The process of money creation can be represented by the multiplier model of money in traditional economics. From this model, it can be known that the required reserve ratio set by the central bank is one of the main determinants of the monetary aggregate and under some assumptions the monetary aggregate can be expressed as the product of the monetary base and the required reserve ratio in steady state. Taking the role that the required reserve ratio plays in the monetary system into account, we developed a random transfer model by introducing a fractional reserve banking system and carried out some simulations to observe how the monetary aggregate evolves over time, how monetary wealth is distributed among agents, as well as how fast money is transferred in the transferring process. Monetary wealth is found to follow asymmetric Laplace distribution, and the fact that latency time of money follows exponential distribution indicates that the transferring process is Poisson type. The theoretical formulas of monetary wealth distribution and the velocity of money in terms of the required reserve ratio are given respectively which are in a good agreement with the simulation results.

Recently, in order to explore the mechanism behind wealth or income distribution, several models have been proposed by applying principles of statistical mechanics. These models share some characteristics, such as consisting of a group of individual agents, a pile of money and a specific trading rule. Whatever the trading rule is, the most noteworthy fact is that money is always transferred from one agent to another in the transferring process. So we call them money transfer models. Besides explaining income and wealth distributions, money transfer models can also be applied to other disciplines. In this paper we summarize these areas as statistical distribution, economic mobility, transfer rate and money creation. First, money distribution (or income distribution) can be exhibited by recording the money stock (flow). Second, the economic mobility can be shown by tracing the change in wealth or income over time for each agent. Third, the transfer rate of money and its determinants can be analyzed by tracing the transferring process of each one unit of money. Finally, money creation process can also be investigated by permitting agents go into debts. Some future extensions to these models are anticipated to be structural improvement and generalized mathematical analysis.

We study a simple model of capital exchange among economic agents in which the effect of a correlation between wealth and connectivity is considered within two different hypotheses: a) agents interact within their own social or economic class and b) agent’s connectivity is related to its success in exchange transactions. The wealth distribution in the first case may generate a two-class society with a clear gap in the middle and highly unequal power law distributions with a great number of strongly impoverished agents and a few very rich ones. In the second case the wealth distribution is modified by the dynamics of the lattice, getting closer to a power law for some values of the parameters of the model. As expected, the lattice itself is different from the random initial one.