英文标题：
《Kinetic models for goods exchange in a multi-agent market》
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作者：
Carlo Brugna and Giuseppe Toscani
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最新提交年份：
2017
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英文摘要：
We introduce a system of kinetic equations describing an exchange market consisting of two populations of agents (dealers and speculators) expressing the same preferences for two goods, but applying different strategies in their exchanges. We describe the trading of the goods by means of some fundamental rules in price theory, in particular by using Cobb-Douglas utility functions for the exchange. The strategy of the speculators is to recover maximal utility from the trade by suitably acting on the percentage of goods which are exchanged. This microscopic description leads to a system of linear Boltzmann-type equations for the probability distributions of the goods on the two populations, in which the post-interaction variables depend from the pre-interaction ones in terms of the mean quantities of the goods present in the market. In this case, it is shown analytically that the strategy of the speculators can drive the price of the two goods towards a zone in which there is a marked utility for their group. Also, the general system of nonlinear kinetic equations of Boltzmann type for the probability distributions of the goods on the two populations is described in details. Numerical experiments then show how the policy of speculators can modify the final price of goods in this nonlinear setting.
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中文摘要：
我们引入了一个动力学方程组，描述了一个由两个代理人（交易商和投机者）组成的交易市场，他们对两种商品表示相同的偏好，但在他们的交易中应用了不同的策略。我们通过价格理论中的一些基本规则来描述商品交易，特别是通过使用交易所的柯布-道格拉斯效用函数。投机者的策略是通过对交换货物的百分比采取适当的行动，从交易中恢复最大效用。这种微观描述导致了两个群体上商品概率分布的线性Boltzmann型方程组，其中，就市场上存在的商品的平均数量而言，互动后变量取决于互动前变量。在这种情况下，分析表明，投机者的策略可以将两种商品的价格推向一个区域，在该区域中，投机者的群体具有显著的效用。此外，还详细描述了两个总体上货物概率分布的Boltzmann型非线性动力学方程的一般系统。数值实验表明，在这种非线性环境下，投机者的政策如何修改商品的最终价格。
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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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