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Analytic treatment of a trading market model

机译:交易市场模型的分析处理

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We mathematically analyze a simple market model where trading at each point in time involves only two agents with the sum of their money being conserved and with neither parties resulting with negative money after the interaction process. The exchange involves random re-distribution among the two players of a fixed fraction of their total money. We obtain a simple integral nonlinear equation for the money distribution. We find that the zero savings and finite savings cases belong to different universality classes. While the zero savings case can be solved analytically, the finite savings solution is obtained by numerically solving the integral equation. We find remarkable agreement with results obtained by other researchers using sophisticated numerical techniques [Chatterjee et al., these proceedings]. [References: 5]
机译:我们用数学方法分析一个简单的市场模型,其中每个时间点的交易只涉及两个代理商,他们的资金被保存下来,在交易过程之后,没有一方产生负钱。交换涉及在两个参与者之间随机重新分配他们总金额的固定部分。我们获得了一个简单的积分非线性方程,用于货币分配。我们发现零储蓄和有限储蓄情况属于不同的普遍性类别。零储蓄的情况可以通过解析来求解,而有限储蓄的解决方案是通过对积分方程进行数值求解而获得的。我们发现与其他研究人员使用复杂的数值技术获得的结果有着显着的一致性[Chatterjee et al。,这些程序]。 [参考:5]

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