经济物理学中的商业周期：总体经济波动、平均风险和平均平方风险
Econophysics of Business Cycles: Aggregate Economic Fluctuations, Mean Risks and Mean Square Risks
AI总结：
本文提出了一种类流体动力学模型，用于描述经济和金融变量的总体波动，通过经济空间中经济主体的风险评级来模拟宏观经济变量，并推导出描述这些变量演变和相互作用的类流体动力学方程。
摘要：
本文提出了一种类流体动力学模型，用于描述经济和金融变量的总体波动。我们通过经济空间中经济主体的风险评级来模拟宏观经济变量，并推导出描述这些变量演变和相互作用的类流体动力学方程。经济或金融变量在经济空间中可能定义出统计矩，如平均风险、平均平方风险等。这些统计矩的波动描述了金融和经济周期的各个阶段。作为例子，我们提出了一个简单的模型关系，用于描述资产与资产收益之间的关系，并推导出描述这些变量演变和相互作用的类流体动力学方程。类流体动力学方程允许推导出描述资产、资产平均风险和资产平均平方风险波动的常微分方程。我们的方法允许描述由任意数量的经济或金融变量相互作用引起的经济周期总体波动。
英文摘要：
This paper presents hydrodynamic-like model of business cycles aggregate fluctuations of economic and financial variables. We model macroeconomics as ensemble of economic agents on economic space and agent's risk ratings play role of their coordinates. Sum of economic variables of agents with coordinate x define macroeconomic variables as functions of time and coordinates x. We describe evolution and interactions between macro variables on economic space by hydrodynamic-like equations. Integral of macro variables over economic space defines aggregate economic or financial variables as functions of time t only. Hydrodynamic-like equations define fluctuations of aggregate variables. Motion of agents from low risk to high risk area and back define the origin for repeated fluctuations of aggregate variables. Economic or financial variables on economic space may define statistical moments like mean risk, mean square risk and higher. Fluctuations of statistical moments describe phases of financial and economic cycles. As example we present a simple model relations between Assets and Revenue-on-Assets and derive hydrodynamic-like equations that describe evolution and interaction between these variables. Hydrodynamic-like equations permit derive systems of ordinary differential equations that describe fluctuations of aggregate Assets, Assets mean risks and Assets mean square risks. Our approach allows describe business cycle aggregate fluctuations induced by interactions between any number of economic or financial variables.
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