Evolutionary model of the growth and size of firms

The key idea of this model is that firms are the result of an evolutionary process. Based on demand and supply considerations the evolutionary model presented here derives explicitly Gibrat’s law of proportionate effects as the result of the competition between products. Applying a preferential attachment mechanism for firms, the theory allows to establish the size distribution of products and firms. Also established are the growth rate and price distribution of consumer goods. Taking into account the characteristic property of human activities to occur in bursts, the model allows also an explanation of the size–variance relationship of the growth rate distribution of products and firms. Further the product life cycle, the learning (experience) curve and the market size in terms of the mean number of firms that can survive in a market are derived. The model also suggests the existence of an invariant of a market as the ratio of total profit to total revenue. The relationship between a neo-classic and an evolutionary view of a market is discussed. The comparison with empirical investigations suggests that the theory is able to describe the main stylized facts concerning the size and growth of firms.     

Minority Game of price promotions in fast moving consumer goods markets

A variation of the Minority Game has been applied to study the timing of promotional actions at retailers in the fast moving consumer goods market. The underlying hypotheses for this work are that price promotions are more effective when fewer than average competitors do a promotion, and that a promotion strategy can be based on past sales data. The first assumption has been checked by analysing 1467 promotional actions for three products on the Dutch market (ketchup, mayonnaise and curry sauce) over a 120-week period, both on an aggregated level and on retailer chain level.

The second assumption was tested by analysing past sales data with the Minority Game. This revealed that high or low competitor promotional pressure for actual ketchup, mayonnaise, curry sauce and barbecue sauce markets is to some extent predictable up to a forecast of some 10 weeks. Whereas a random guess would be right 50% of the time, a single-agent game can predict the market with a success rate of 56% for a 6–9 week forecast. This number is the same for all four mentioned fast moving consumer markets. For a multi-agent game a larger variability in the success rate is obtained, but predictability can be as high as 65%.

Contrary to expectation, the actual market does the opposite of what game theory would predict. This points at a systematic oscillation in the market. Even though this result is not fully understood, merely observing that this trend is present in the data could lead to exploitable trading benefits. As a check, random history strings were generated from which the statistical variation in the game prediction was studied. This shows that the odds are 1:1,000,000 that the observed pattern in the market is based on coincidence.     

Cellular Automata with network incubation in information technology diffusion

Innovation diffusion of network goods determines direct network externalities that depress sales for long periods and delay full benefits. We model this effect through a multiplicative dynamic market potential driven by a latent individual threshold embedded in a special Cellular Automata representation. The corresponding mean field approximation of its aggregate version is a Riccati equation with a closed form solution. This allows the detection of a change-point time separating an incubation period from a subsequent take-off due to a collective threshold (critical mass). Weighted nonlinear least squares are the main inferential methodology. An application is analysed with reference to USA fax machine diffusion.     

The firm as a bundle of barcodes

We empirically investigate the firm growth model proposed by Buldyrev et al. by using a unique dataset that contains the daily sales of more than 200 thousand products, which are collected from about 200 supermarkets in Japan over the last 20 years. We find that the empirical firm growth distribution is characterized by a Laplace distribution at the center and power-law at the tails, as predicted by the model. However, some of these characteristics disappear once we randomly reshuffle products across firms, implying that the shape of the empirical distribution is not produced as described by the model. Our simulation results suggest that the shape of the empirical distribution stems mainly from the presence of relationship between the size of a product and its growth rate.     

Sales distribution of consumer electronics

Using the uniform most powerful unbiased test, we observed the sales distribution of consumer electronics in Japan on a daily basis and report that it follows both a lognormal distribution and a power-law distribution and depends on the state of the market. We show that these switches occur quite often. The underlying sales dynamics found between both periods nicely matched a multiplicative process. However, even though the multiplicative term in the process displays a size-dependent relationship when a steady lognormal distribution holds, it shows a size-independent relationship when the power-law distribution holds. This difference in the underlying dynamics is responsible for the difference in the two observed distributions.     

Evolutionary model of the personal income distribution

The aim of this work is to develop a qualitative picture of the personal income distribution. Treating an economy as a self-organized system the key idea of the model is that the income distribution contains competitive and non-competitive contributions. The presented model distinguishes between three main income classes. 1. Capital income from private firms is shown to be the result of an evolutionary competition between products. A direct consequence of this competition is Gibrat’s law suggesting a lognormal income distribution for small private firms. Taking into account an additional preferential attachment mechanism for large private firms the income distribution is supplemented by a power law (Pareto) tail. 2. Due to the division of labor a diversified labor market is seen as a non-competitive market. In this case wage income exhibits an exponential distribution. 3. Also included is income from a social insurance system. It can be approximated by a Gaussian peak. A consequence of this theory is that for short time intervals a fixed ratio of total labor (total capital) to net income exists (Cobb–Douglas relation). A comparison with empirical high resolution income data confirms this pattern of the total income distribution. The theory suggests that competition is the ultimate origin of the uneven income distribution.     

Consumers don’t play dice,influence of social networks and advertisements

Empirical data of supermarket sales show stylised facts that are similar to stock markets, with a broad (truncated) Lévy distribution of weekly sales differences in the baseline sales [R.D. Groot, Physica A 353 (2005) 501]. To investigate the cause of this, the influence of social interactions and advertisements are studied in an agent-based model of consumers in a social network. The influence of network topology was varied by using a small-world network, a random network and a Barabási–Albert network. The degree to which consumers value the opinion of their peers was also varied.On a small-world and random network we find a phase transition between an open market and a locked-in market that is similar to condensation in liquids. At the critical point, fluctuations become large and buying behaviour is strongly correlated. However, on the small world network the noise distribution at the critical point is Gaussian, and critical slowing down occurs which is not observed in supermarket sales. On a scale-free network, the model shows a transition between a gas-like phase and a glassy state, but at the transition point the noise amplitude is much larger than what is seen in supermarket sales.To explore the role of advertisements, a model is studied where imprints are placed on the minds of consumers that ripen when a decision for a product is made. The correct distribution of weekly sales returns follows naturally from this model, as well as the noise amplitude, the correlation time and cross-correlation of sales fluctuations. For particular parameter values, simulated sales correlation shows power-law decay in time. The model predicts that social interaction helps to prevent aversion, and that products are viewed more positively when their consumption rate is higher.     

Power law tails in the Italian personal income distribution

We investigate the shape of the Italian personal income distribution using microdata from the Survey on Household Income and Wealth, made publicly available by the Bank of Italy for the years 1977–2002. We find that the upper tail of the distribution is consistent with a Pareto-power law type distribution, while the rest follows a two-parameter lognormal distribution. The results of our analysis show a shift of the distribution and a change of the indexes specifying it over time. As regards the first issue, we test the hypothesis that the evolution of both gross domestic product and personal income is governed by similar mechanisms, pointing to the existence of correlation between these quantities. The fluctuations of the shape of income distribution are instead quantified by establishing some links with the business cycle phases experienced by the Italian economy over the years covered by our dataset.     

Exact Solution of Fractional Diffusion Model with Source Term used in Study of Concentration of Fission Product in Uranium Dioxide Particle

The exact solution of fractional diffusion model with a location-independent source term used in the study of the concentration of fission product in spherical uranium dioxide (UO₂) particle is built. The adsorption effect of the fission product on the surface of the UO₂ particle and the delayed decay effect are also considered. The solution is given in terms of Mittag-Leffler function with finite Hankel integral transformation and Laplace transformation. At last, the reduced forms of the solution under some special physical conditions, which is used in nuclear engineering, are obtained and corresponding remarks are given to provide significant exact results to the concentration analysis of nuclear fission products in nuclear reactor.     

Model of wealth and goods dynamics in a closed market

A simple computer simulation model of a closed market on a fixed network with free flow of goods and money is introduced. The model contains only two variables: the amount of goods and money beside the size of the system. An initially flat distribution of both variables is presupposed. We show that under completely random rules, i.e. through the choice of interacting agent pairs on the network and of the exchange rules that the market stabilizes in time and shows diversification of money and goods. We also indicate that the difference between poor and rich agents increases for small markets, as well as for systems in which money is steadily deduced from the market through taxation. It is also found that the price of goods decreases when taxes are introduced, likely due to the less availability of money.     

Fractional nonlinear diffusion equation and first passage time

We investigate the solutions and the first passage time for anomalous diffusion processes governed by the fractional nonlinear diffusion equation with a space- and time-dependent diffusion coefficient subject to absorbing boundaries and the initial condition. We obtain explicit analytical expression for the probability distribution, the first passage time distribution, the mean first passage time, and the mean squared displacement corresponding to different time-dependent diffusion coefficient. In addition, we compare our results for the first passage time distribution and the mean first passage time with the one obtained by usual linear diffusion equation with time-dependent diffusion coefficient.     

Molecular evolution under fitness fluctuations

Molecular evolution is a stochastic process governed by fitness, mutations, and reproductive fluctuations in a population. Here, we study evolution where fitness itself is stochastic, with random switches in the direction of selection at individual genomic loci. As the correlation time of these fluctuations becomes larger than the diffusion time of mutations within the population, fitness changes from an annealed to a quenched random variable. We show that the rate of evolution has its maximum in the crossover regime, where both time scales are comparable. Adaptive evolution emerges in the quenched fitness regime (evidence for such fitness fluctuations has recently been found in genomic data). The joint statistical theory of reproductive and fitness fluctuations establishes a conceptual connection between evolutionary genetics and statistical physics of disordered systems.     

基于信息分配和扩散理论的东北地区干旱脆弱性特征分析

基于信息分配和扩散理论, 结合标准化降水指数和东北三省(黑龙江、吉林、辽宁)旱灾灾损指数, 综合考虑了气象因子与社会因子, 分析了我国东北三省1971–2012年的干旱脆弱性特征, 并进一步计算了我国东北三省的干旱风险. 使用信息分配方法估计干旱强度概率分布, 采用二维正态信息扩散方法构造了干旱强度与旱灾灾损的脆弱性关系, 将干旱强度的概率分布与脆弱性折线相乘求和(离散分布)或积分(连续分布)即可得到多年平均风险. 研究表明, 针对灾损的小样本事件引入信息分配和扩散方法对小样本数据进行分析, 获取的干旱强度概率分布比简单直方图法所得更加平滑, 而以事件为因、灾损为果得到干旱强度-旱灾灾损的脆弱性关系, 物理意义明确, 所得脆弱性关系折线也比较符合实际情况, 并且不同样本长度所得结果相近, 对样本长度不敏感, 较好地克服了小样本分析的不稳定性. 关键词： 信息分配和扩散理论 标准化降水指数 脆弱性 风险     

Quantifying price fluctuations in the Brazilian stock market

This paper investigates price fluctuations in the Brazilian stock market. We employ a recently developed methodology to test whether the Brazilian stock price returns present a power law distribution and find that we cannot reject such behavior. Empirical results for sub-partitions of the time series suggests that for most of the time the power law is not rejected, but that in some cases the data set does not conform with a power law distribution.     

基于鲁棒回声状态网络的混沌时间序列预测研究

针对回声状态网络模型易受异常点影响的问题, 提出一种基于拉普拉斯先验分布的鲁棒回声状态网络模型. 通过采用对异常点不敏感的拉普拉斯分布代替高斯分布作为模型输出的先验, 以增强网络对于异常点的抑制能力. 此外, 为解决由引入拉普拉斯分布所造成的求解困难的问题, 根据边际优化方法, 构建适当的替代函数, 使拉普拉斯先验等价转化为易于计算的高斯形式, 并通过贝叶斯方法实现模型参数的自适应估计. 仿真结果表明, 在异常点存在的情况下, 本文所提出的模型具有较好的鲁棒性, 并仍能保持较高的预测精度. 关键词： 回声状态网络 鲁棒模型 替代函数 拉普拉斯分布     

多孔材料分形扩散模型的Fourier-Bessel级数算法及其应用

将Fick扩散定律的Fourier三角级数算法推广成多孔材料分形扩散模型的Fourier-Bessel级数算法,并把它应用于化学工程中吸附问题涉及的浓度分布与相对吸附量的计算中,取得一些规律性认识.由于分形扩散模型是在Fick扩散定律的基础上增加了表征微观结构的参数d_f和θ,研究多孔材料中的浓度分布与相对吸附量时,与Fick扩散定律的研究结果相比,定性上基本一致,在定量上有差别,d_f和θ对扩散传质过程的影响各有侧重,用它们可更好地描述多孔材料中的扩散过程.     

Pattern formation in superdiffusion Oregonator model

Pattern formations in an Oregonator model with superdiffusion are studied in two-dimensional(2D) numerical simulations. Stability analyses are performed by applying Fourier and Laplace transforms to the space fractional reaction–diffusion systems. Antispiral, stable turing patterns, and travelling patterns are observed by changing the diffusion index of the activator. Analyses of Floquet multipliers show that the limit cycle solution loses stability at the wave number of the primitive vector of the travelling hexagonal pattern. We also observed a transition between antispiral and spiral by changing the diffusion index of the inhibitor.     

Moving average rules as a source of market instability

Despite the pervasiveness of the efficient markets paradigm in the academic finance literature, the use of various moving average (MA) trading rules remains popular with financial market practitioners. This paper proposes a stochastic dynamic financial market model in which demand for traded assets has both a fundamentalist and a chartist component. The chartist demand is governed by the difference between current price and a (long-run) MA. Our simulations show that the MA is a source of market instability, and the interaction of the MA and market noises can lead to the tendency for the market price to take long excursions away from the fundamental. The model reveals various market price phenomena, the coexistence of apparent market efficiency and a large chartist component, price resistance levels, long memory and skewness and kurtosis of returns.     

A reaction–diffusion model for market fluctuations – A relation between price change and traded volumes

Two decades ago Bak et al. (1997) [3] proposed a reaction–diffusion model to describe market fluctuations. In the model buyers and sellers diffuse from opposite ends of a 1D interval that represents a price range. Trades occur when buyers and sellers meet. We show analytically and numerically that the model well reproduces the square-root relation between traded volumes and price changes that is observed in real-life markets. The result is remarkable as this relation has commonly been explained in terms of more elaborate trader strategies. We furthermore explain why the square-root relation is robust under model modifications and we show how real-life bond market data exhibit the square-root relation.