物理学在金融和经济学中的应用：回报，交易活动和收入
Applications of physics to finance and economics: returns, trading activity and income
摘要：
本论文报告了物理方法应用于金融和经济问题的工作。第一部分研究股票市场数据（第1章至第5章）。第二部分专门讨论美国的个人收入（第6章）。我们首先研究了股票收益率在中观时间滞后（回报水平）的概率分布，范围从大约一个小时到大约一个月。对于介观时间，大部分分布（超过99%的概率）遵循指数律。在较长的时间，指数规律不断演变成高斯分布。在刻画了股票收益率的中观时滞特征后，我们研究了从属性假说。由交易次数过程构造的综合波动率V_t可以作为布朗运动的从属变量。这种从属关系能够描述大约85%的股票回报率，其时间滞后从1小时开始，但短于一天。最后，我们证明了CIR过程能够很好地描述经验V_t过程，从而使得相应的Heston模型能够以隶属度所允许的最大质量近似地描述对数收益率x_t过程。最后，我们研究了个人收入分配的时间演变。我们发现，美国的个人收入分配具有明确的两个收入阶层结构。大多数人口（97-99%）属于低收入阶层，其特征是指数Boltzmann-Gibb（“热”）分布，而高收入阶层（1-3%的人口）则具有帕累托幂律（"超热“）分布。我们表明，“热”的一部分是固定的时间。
英文摘要：
This dissertation reports work where physics methods are applied to financial and economical problems. The first part studies stock market data (chapter 1 to 5). The second part is devoted to personal income in the USA (chapter 6). We first study the probability distribution of stock returns at mesoscopic time lags (return horizons) ranging from about an hour to about a month. For mesoscopic times the bulk of the distribution (more than 99% of the probability) follows an exponential law. At longer times, the exponential law continuously evolves into Gaussian distribution. After characterizing the stock returns at mesoscopic time lags, we study the subordination hypothesis. The integrated volatility V_t constructed from the number of trades process can be used as a subordinator for a Brownian motion. This subordination is able to describe approximatly 85% of the stock returns for time lags that start at 1 hour but are shorter than one day. Finally, we show that the CIR process describes well enough the empirical V_t process, such that the corresponding Heston model is able to describe the log-returns x_t process, with approximately the maximum quality that the subordination allows. Finally, we study the time evolution of the personal income distribution. We find that the personal income distribution in the USA has a well-defined two-income-class structure. The majority of population (97-99%) belongs to the lower income class characterized by the exponential Boltzmann-Gibb(``thermal'') distribution, whereas the higher income class (1-3% of population) has a Pareto power-law (``superthermal'') distribution. We show that the ``thermal'' part is stationary in time.
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