本文關(guān)鍵詞： 復(fù)雜經(jīng)濟(jì)系統(tǒng) 復(fù)雜網(wǎng)絡(luò) 經(jīng)濟(jì)物理學(xué) 收入分布 公司規(guī)模分布 冪律分布 無標(biāo)度　出處：《華中師范大學(xué)》2016年博士論文　論文類型：學(xué)位論文

【摘要】：經(jīng)濟(jì)物理學(xué)作為一個(gè)新興的、跨學(xué)科的研究領(lǐng)域,近年來吸引了很多物理學(xué)家以及經(jīng)濟(jì)學(xué)家的注意,運(yùn)用基于統(tǒng)計(jì)物理的統(tǒng)計(jì)金融方面的知識(shí)來研究金融、經(jīng)濟(jì)市場(chǎng)常常能起到很好的作用。本文主要研究了經(jīng)濟(jì)市場(chǎng)中個(gè)體收入分布的統(tǒng)計(jì)特性。通過理論模型的數(shù)值分析和Monte Carlo模擬,將理論分析結(jié)果和模擬結(jié)果與實(shí)證研究對(duì)比,探討了中國(guó)個(gè)人收入分布以及公司規(guī)模分布的性質(zhì)。我們采用樣本量較大、觀測(cè)年份較長(zhǎng)的實(shí)證數(shù)據(jù)研究了中國(guó)的個(gè)人收入分布。運(yùn)用最大似然法,對(duì)中國(guó)個(gè)人收入分布進(jìn)行了擬合,得到了與國(guó)外發(fā)達(dá)國(guó)家基本一致的特性:中、低收入人群的個(gè)人收入符合log-normal分布;而高收入部分則滿足冪律分布。為了驗(yàn)證實(shí)證分析結(jié)果的準(zhǔn)確性,對(duì)全部觀測(cè)年份的收入數(shù)據(jù)進(jìn)行了擬合,也發(fā)現(xiàn)了類似的兩段式收入分布。在對(duì)擬合參數(shù)分析時(shí)發(fā)現(xiàn),隨著觀測(cè)年份的推移,中、低收入部分的log-normal指數(shù)逐漸增大,而高收入部分的冪律指數(shù)則無明顯變化趨勢(shì)。與國(guó)外發(fā)達(dá)國(guó)家相比,中國(guó)個(gè)人收入分布的冪律指數(shù)相對(duì)較大。分析了中國(guó)的公司規(guī)模以及增長(zhǎng)率分布。用資產(chǎn)和員工數(shù)作為公司的規(guī)模指標(biāo),分別分析了二者的分布。擬合顯示這兩項(xiàng)指標(biāo)的分布均符合冪律分布,其中員工數(shù)分布具有較大的冪律指數(shù),二者的冪律指數(shù)在全部觀測(cè)年間均無明顯變化。對(duì)函數(shù)形式特點(diǎn)不明的公司增長(zhǎng)率分布,通過Subbotin family函數(shù)的擬合,發(fā)現(xiàn)公司資產(chǎn)和員工數(shù)的增長(zhǎng)率分布均符合Laplace分布,而非Gaussian分布。分析了公司增長(zhǎng)率的標(biāo)準(zhǔn)方差與公司規(guī)模之間的標(biāo)度關(guān)系,與Stanley在美國(guó)公司數(shù)據(jù)中發(fā)現(xiàn)的標(biāo)度關(guān)系類似。公司資產(chǎn)和員工數(shù)增長(zhǎng)率的標(biāo)準(zhǔn)方差均為公司規(guī)模的冪律函數(shù)。另外,在增長(zhǎng)率的標(biāo)準(zhǔn)方差與公司開業(yè)年份之間同樣也存在冪律的標(biāo)度關(guān)系。提出了包含長(zhǎng)程相互作用的隨機(jī)交易模型。為了與實(shí)證數(shù)據(jù)分析相比較,首先運(yùn)用平均場(chǎng)的方法對(duì)模型進(jìn)行了分析,當(dāng)不考慮加法擴(kuò)散過程時(shí),得到了高收入部分的冪律分布。隨后,討論了 網(wǎng)絡(luò)上的長(zhǎng)程隨機(jī)交易過程,假定個(gè)體i和j之間交易的財(cái)富量為個(gè)體i的連接度ki以及它們之間最短路徑dj的函數(shù),即交易量Qij = (qo)/(kidij),其中qo為常量。并將個(gè)體交易收入之外的財(cái)富作為加法擴(kuò)散過程。發(fā)現(xiàn)在均勻網(wǎng)絡(luò)上,系統(tǒng)的收入分布與網(wǎng)絡(luò)的平均度相關(guān),符合高斯分布或者泊松分布;而在非均勻網(wǎng)絡(luò)上,收入分布則與網(wǎng)絡(luò)的連接度分布一致,滿足冪律分布。分析了兩人兩策略博弈模型在網(wǎng)絡(luò)上的演化過程,討論了在均勻混合種群中,個(gè)體收益與合作者比例演化的關(guān)系。以囚徒困境模型為例,探討了無標(biāo)度網(wǎng)絡(luò)上的演化博弈,得到了種群的收入分布與網(wǎng)絡(luò)連接度分布之間的函數(shù)關(guān)系。在復(fù)雜網(wǎng)絡(luò)上對(duì)兩種收入分布模型進(jìn)行了Monte Carlo模擬。首先是長(zhǎng)程隨機(jī)交易模型,在BA無標(biāo)度網(wǎng)絡(luò)、靜態(tài)無標(biāo)度網(wǎng)絡(luò)以及小世界網(wǎng)絡(luò)上的研究發(fā)現(xiàn),個(gè)體的財(cái)富交易主要依賴于鄰居間的相互作用,收入分布與網(wǎng)絡(luò)的連接度分布高度相關(guān),長(zhǎng)程相互作用被局部交易所覆蓋。討論了二分網(wǎng)絡(luò)上的隨機(jī)交易模型,將城鎮(zhèn)居民和農(nóng)村居民看作二分網(wǎng)絡(luò)上的兩類節(jié)點(diǎn),發(fā)現(xiàn)收入分布符合一種雙峰分布,且系統(tǒng)穩(wěn)定后,農(nóng)村居民的平均收入有所增長(zhǎng)。在靜態(tài)無標(biāo)度網(wǎng)絡(luò)上進(jìn)行了囚徒困境博弈模型和雪堆博弈模型的模擬。通過網(wǎng)絡(luò)上的博弈過程,兩種博弈模型均得到了冪律形式的收益分布。對(duì)于異質(zhì)性程度不同的無標(biāo)度網(wǎng)絡(luò),收益分布的冪律指數(shù)無明顯變化。
[Abstract]:Economic physics as an emerging, interdisciplinary research field in recent years, attracted a lot of attention of physicists and economists, financial statistics using statistical physics based knowledge to study finance, financial markets often can play a good role. This paper mainly studies the statistical characteristics of individual income distribution in the market economy. By numerical analysis and Monte Carlo model simulation, the comparison between theoretical analysis and simulation results and empirical research, discusses the Chinese personal income distribution and company size distribution properties. We use a large amount of samples, the empirical data of the year long observation of personal income distribution China. Using the maximum likelihood method for personal China the income distribution of the fitting, get the characteristics consistent with the developed countries, the low income crowd: personal income in accordance with log-no Rmal distribution; and the high income part meet the power-law distribution. In order to validate the results of the empirical analysis, the income data of all observed years fitted, found a similar two segment income distribution. Based on the analysis of the fitting parameters, with the observation year goes on, in low income part the log-normal index increased gradually, and the power-law index of high income is no obvious trend. Compared with the developed countries, the income distribution of power-law index is relatively large. China personal analysis of China company size and growth rate distribution. With assets and number of employees as the scale index, respectively, analyzes the distribution of the two the fitting shows the distribution of these two indicators are in line with the power-law distribution, the number of employees with the distribution of power-law index is larger, the power-law index of the two did not change significantly in all years. The function of observation The form characteristics of unknown company growth rate distribution, by fitting the Subbotin family function, found that the company assets and number of employees, the growth rate distribution conformed to Laplace distribution, and Gaussian distribution. To analyze the relationship between corporate growth rate standard deviation and the scale of the company scale, similar to the Stanley company in the United States found in the data standard the relationship between the growth rate of the company's assets. The standard deviation and the number of employees are power law function of the size of the company. In addition, the relationship between years there is also a power-law scaling in the growth rate of the standard deviation of business with the company. Put forward the stochastic trading model including the long-range interaction. In order to analysis and empirical data comparison first of all, the model is analyzed by using the method of mean field, when not considering the addition of the diffusion process, the power-law distribution of high income part. Then, discusses on the network long Cheng Sui For the transaction process, assuming the amount of wealth transactions between individual I and j as a function of connectivity between individual ki I and their DJ shortest path, namely the trading volume of Qij = (Qo) / (kidij), where Qo is a constant. And the individual trading income wealth as a diffusion process. The addition of uniform network, income distribution and the average degree of the network system, in line with the Gauss distribution or Poisson distribution; and in heterogeneous network, the connection degree distribution of income distribution is consistent with a network of, meet the power-law distribution. Analysis of the two two game model evolution on the network, discussed in the mixed population, the relationship between individual income and the proportion of cooperative evolution. In the prisoner's dilemma model as an example, discusses the evolutionary game of scale-free network, the function of income distribution and population distribution network connectivity relationship. In complex networks Two kinds of income distribution model and Monte Carlo simulation. The first is the long-range random trading model, the BA scale-free network, the static research on scale free networks and small world networks found that the interaction of individual wealth trading mainly depends on the connection between neighbors, is highly correlated with income distribution and degree distribution network, long-range interactions are local exchange coverage. This paper discusses stochastic trading model of two points on the network, the urban residents and rural residents as two class two nodes on the network, found that the income distribution in line with a Shuangfeng distribution, and the system is stable, the average income of rural residents increased. In the static scale-free the network simulates the prisoner's dilemma game model and the snowdrift game model. Through the process of network game, two game models are the return distribution of power-law form for different degree of heterogeneity. There is no obvious change in the power law index of the income distribution in the scale-free network.

【學(xué)位授予單位】：華中師范大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：F126.2;O157.5

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