摘要翻译：
从贸易互动中衍生出来的保守财富交换过程被建模为价值的乘性随机转移，其中每一次互动使两个干预者中最贫穷者的财富乘以一个随机增益eta=(1+kappa)，而kappa是一个随机回报。通过对财富分布P(w，t)的动力学方程的分析，得到了任意收益分布pi(kappa)的一般性质。如果增益的几何平均值大于1，即<lneta>>0，则在长时间内得到一个非平凡的均衡财富分布P(w)。另一方面，当<lneta><0时，就会发生财富凝聚，这意味着从长期来看，单个代理人获得了全部财富。即使差剂的平均回报<kappa>为正，也会发生这种浓缩现象。在稳定相中，当w->0时，P(w)表现为w^{(T-1)}，我们精确地求出T。该指数在稳定相不为零，但在接近凝聚界面时趋于零。对于凯利下注的特殊情况，精确的财富分布可以通过解析得到，而且是指数分布。然而，我们表明，无论π（kappa）是多少，我们的模型都是不可逆的。在凝聚相中，相对秩为x的试剂在有限次t下的财富为w(x,t)\sim e^{x t<lneta>}。因此，在有限的时间里，财富分配是P(w)\sim1/w，而在大量时间里，所有的财富最终都在一个代理人手中。进行了数值模拟，结果与上述分析结果比较令人满意。
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英文标题：
《Multiplicative Asset Exchange with Arbitrary Return Distributions》
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作者：
Cristian F. Moukarzel
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最新提交年份：
2011
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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：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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英文摘要：
  The conservative wealth-exchange process derived from trade interactions is modeled as a multiplicative stochastic transference of value, where each interaction multiplies the wealth of the poorest of the two intervening agents by a random gain eta=(1+kappa), with kappa a random return. Analyzing the kinetic equation for the wealth distribution P(w,t), general properties are derived for arbitrary return distributions pi(kappa). If the geometrical average of the gain is larger than one, i.e. if <ln eta> >0, in the long time limit a nontrivial equilibrium wealth distribution P(w) is attained. Whenever <ln eta> <0, on the other hand, Wealth Condensation occurs, meaning that a single agent gets the whole wealth in the long run. This concentration phenomenon happens even if the average return <kappa> of the poor agent is positive. In the stable phase, P(w) behaves as w^{(T-1)} for w -> 0, and we find T exactly. This exponent is nonzero in the stable phase but goes to zero on approach to the condensation interface. The exact wealth distribution can be obtained analytically for the particular case of Kelly betting, and it turns out to be exponential. We show, however, that our model is never reversible, no matter what pi(kappa) is. In the condensing phase, the wealth of an agent with relative rank x is found to be w(x,t) \sim e^{x t <ln eta>} for finite times t. The wealth distribution is consequently P(w) \sim 1/w for finite times, while all wealth ends up in the hands of a single agent for large times. Numerical simulations are carried out, and found to satisfactorily compare with the above mentioned analytic results.
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PDF链接：
https://arxiv.org/pdf/1108.0386