英文标题：
《Evolution of wealth in a nonconservative economy driven by local Nash
equilibria》
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作者：
Pierre Degond, Jian-Guo Liu, Christian Ringhofer
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最新提交年份：
2014
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英文摘要：
We develop a model for the evolution of wealth in a non-conservative economic environment, extending a theory developed earlier by the authors. The model considers a system of rational agents interacting in a game theoretical framework. This evolution drives the dynamic of the agents in both wealth and economic configuration variables. The cost function is chosen to represent a risk averse strategy of each agent. That is, the agent is more likely to interact with the market, the more predictable the market, and therefore the smaller its individual risk. This yields a kinetic equation for an effective single particle agent density with a Nash equilibrium serving as the local thermodynamic equilibrium. We consider a regime of scale separation where the large scale dynamics is given by a hydrodynamic closure with this local equilibrium. A class of generalized collision invariants (GCIs) is developed to overcome the difficulty of the non-conservative property in the hydrodynamic closure derivation of the large scale dynamics for the evolution of wealth distribution. The result is a system of gas dynamics-type equations for the density and average wealth of the agents on large scales. We recover the inverse Gamma distribution, which has been previously considered in the literature, as a local equilibrium for particular choices of the cost function.
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中文摘要：
我们发展了一个非保守经济环境下财富演化的模型，扩展了作者早期发展的理论。该模型考虑了理性主体在博弈论框架下的互动系统。这种演变推动了财富和经济结构变量中代理人的动态变化。选择成本函数来表示每个代理的风险规避策略。也就是说，代理人更有可能与市场互动，市场越可预测，因此其个人风险越校这就产生了一个有效单颗粒药剂密度的动力学方程，其中纳什平衡作为局部热力学平衡。我们考虑了一个尺度分离的区域，其中大尺度动力学由具有该局部平衡的水动力闭合给出。为了克服财富分布演化大尺度动力学的流体动力学闭包推导中的非保守性困难，提出了一类广义碰撞不变量。结果是一个气体动力学类型方程组，用于计算大尺度上的介质密度和平均财富。我们恢复了先前文献中考虑过的逆伽马分布，作为成本函数特定选择的局部均衡。
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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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