英文标题：
《The Immediate Exchange model: an analytical investigation》
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作者：
Guy Katriel
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最新提交年份：
2014
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英文摘要：
We study the Immediate Exchange model, recently introduced by Heinsalu and Patriarca [Eur. Phys. J. B 87: 170 (2014)], who showed by simulations that the wealth distribution in this model converges to a Gamma distribution with shape parameter $2$. Here we justify this conclusion analytically, in the infinite-population limit. An infinite-population version of the model is derived, describing the evolution of the wealth distribution in terms of iterations of a nonlinear operator on the space of probability densities. It is proved that the Gamma distributions with shape parameter $2$ are fixed points of this operator, and that, starting with an arbitrary wealth distribution, the process converges to one of these fixed points. We also discuss the mixed model introduced in the same paper, in which exchanges are either bidirectional or unidirectional with fixed probability. We prove that, although, as found by Heinsalu and Patriarca, the equilibrium distribution can be closely fit by Gamma distributions, the equilibrium distribution for this model is {\\it{not}} a Gamma distribution.
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中文摘要：
我们研究了Heinsalu和Patriarca[Eur.Phys.J.B 87:170（2014）]最近提出的即时交换模型，他们通过模拟表明，该模型中的财富分布收敛于形状参数为$2$的伽马分布。在这里，我们用解析的方法证明了这个结论，在无限的人口极限下。导出了该模型的无限人口版本，用概率密度空间上非线性算子的迭代来描述财富分布的演化。证明了形状参数为$2$的伽马分布是该算子的不动点，并且从任意财富分布开始，该过程收敛到其中一个不动点。我们还讨论了在同一篇文章中引入的混合模型，其中交换是双向的或单向的，具有固定的概率。我们证明，尽管正如海因萨鲁和帕特里亚卡所发现的，平衡分布可以用伽马分布紧密拟合，但这个模型的平衡分布是{it{not}}伽马分布。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：General Finance 一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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一级分类：Physics 物理学
二级分类：Adaptation and Self-Organizing Systems 自适应和自组织系统
分类描述：Adaptation, self-organizing systems, statistical physics, fluctuating systems, stochastic processes, interacting particle systems, machine learning
自适应，自组织系统，统计物理，波动系统，随机过程，相互作用粒子系统，机器学习
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