资金转移模型的动态过程
Dynamic Process of Money Transfer Models
摘要：
我们用数值方法研究了一些转移模型中动态现象的统计力学，包括货币流通和经济流动。我们所研究的模型是A. Dragulescu和V.Yakovenko [1]，A. Chakraborti和B.K. Chakrabarti [2]及其具有不同储蓄率的扩展模型[3]。流通速度与货币的平均持有时间呈负相关。为了检验这些模型中货币转移过程的本质，我们给出了持有时间的概率分布。在均匀储蓄率模型中，分布服从指数规律，这表明这里的货币转移是一种泊松过程。而当储蓄率设定不同时，持有时间的分布服从幂律。速度也可以从一个典型的个人的最佳选择推导出来。为建立速度的微观基础提供了一种途径。为了揭示微观分布背后的动力机制，我们通过收集代理人的排名时间序列来考察流动性，并采用经济学家提出的一个指标来衡量。在均匀储蓄率模型中，储蓄率越高，经济主体在经济中的行动越慢。与此同时，所有的经纪人都有同样的机会成为富人。然而，在储蓄率不同的模型中，假设经济存在分层现象，这就不成立了。同时，本文也展示了代理人等级的波动率分布，以区分不同模型之间的差异。
英文摘要：
We have studied numerically the statistical mechanics of the dynamic phenomena, including money circulation and economic mobility, in some transfer models. The models on which our investigations were performed are the basic model proposed by A. Dragulescu and V. Yakovenko [1], the model with uniform saving rate developed by A. Chakraborti and B.K. Chakrabarti [2], and its extended model with diverse saving rate [3]. The velocity of circulation is found to be inversely related with the average holding time of money. In order to check the nature of money transferring process in these models, we demonstrated the probability distributions of holding time. In the model with uniform saving rate, the distribution obeys exponential law, which indicates money transfer here is a kind of Poisson process. But when the saving rate is set diversely, the holding time distribution follows a power law. The velocity can also be deduced from a typical individual's optimal choice. In this way, an approach for building the micro-foundation of velocity is provided. In order to expose the dynamic mechanism behind the distribution in microscope, we examined the mobility by collecting the time series of agents' rank and measured it by employing an index raised by economists. In the model with uniform saving rate, the higher saving rate, the slower agents moves in the economy. Meanwhile, all of the agents have the same chance to be the rich. However, it is not the case in the model with diverse saving rate, where the assumed economy falls into stratification. The volatility distribution of the agents' ranks are also demonstrated to distinguish the differences among these models.
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