英文标题：
《A stylized model for wealth distribution》
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作者：
Bertram D\\\"uring, Nicos Georgiou, Enrico Scalas
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最新提交年份：
2021
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英文摘要：
The recent book by T. Piketty (Capital in the Twenty-First Century) promoted the important issue of wealth inequality. In the last twenty years, physicists and mathematicians developed models to derive the wealth distribution using discrete and continuous stochastic processes (random exchange models) as well as related Boltzmann-type kinetic equations. In this literature, the usual concept of equilibrium in Economics is either replaced or completed by statistical equilibrium. In order to illustrate this activity with a concrete example, we present a stylised random exchange model for the distribution of wealth. We first discuss a fully discrete version (a Markov chain with finite state space). We then study its discrete-time continuous-state-space version and we prove the existence of the equilibrium distribution. Finally, we discuss the connection of these models with Boltzmann-like kinetic equations for the marginal distribution of wealth. This paper shows in practice how it is possible to start from a finitary description and connect it to continuous models following Boltzmann\'s original research program.
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中文摘要：
T.Piketty（二十一世纪的资本）最近的一本书提出了财富不平等的重要问题。在过去二十年中，物理学家和数学家利用离散和连续随机过程（随机交换模型）以及相关的Boltzmann型动力学方程开发了模型来推导财富分布。在这篇文献中，经济学中通常的均衡概念要么被统计均衡所取代，要么被统计均衡所完善。为了用一个具体的例子来说明这一活动，我们提出了一个用于财富分配的风格化随机交换模型。我们首先讨论一个完全离散的版本（具有有限状态空间的马尔可夫链）。然后，我们研究了它的离散时间连续状态空间版本，并证明了平衡分布的存在性。最后，我们讨论了这些模型与财富边际分布的类玻耳兹曼动力学方程之间的联系。本文在实践中展示了如何从有限描述开始，并按照Boltzmann最初的研究计划将其连接到连续模型。
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分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Physics 物理学
二级分类：Physics and Society 物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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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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