财富分配的程式化模型
A stylized model for wealth distribution
摘要：
最近的一本书由T。皮凯蒂（《21世纪资本论》）提出了财富不平等的重要问题。在过去的二十年里，物理学家和数学家开发了模型，使用离散和连续随机过程（随机交换模型）以及相关的玻尔兹曼型动力学方程来推导财富分布。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，要么被统计均衡所补充。为了用一个具体的例子来说明这一活动，我们提出了一个程式化的随机交换模型的财富分配。我们首先讨论一个完全离散的版本（一个马尔可夫链有限状态空间）。然后，我们研究其离散时间连续状态空间的版本，我们证明了存在的平衡分布。最后，我们讨论了这些模型与玻尔兹曼动力学方程的边缘分布的财富。本文表明，在实践中，它是如何可能从有限的描述，并将其连接到连续模型以下玻尔兹曼的原始研究计划。
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
