摘要翻译：
本文给出了一种具有任意多个代理的经济系统的分析方法，它跟踪了系统的相互作用和代理的复杂性。这种形式主义并不寻求聚合代理人。它用对整个系统和Agent行为的概率描述取代了标准的优化方法。这是在两个不同的步骤中完成的。第一步考虑了一个包含任意多个Agent的相互作用系统，其中每个Agent的效用函数都受到不可预测的冲击。在这样的环境下，不需要解决个别的优化问题。每个智能体都是以其效用最优为中心的时间相关概率分布来描述的。因此，整个智能体系统是由一个取决于时间、智能体相互作用和前瞻性行为的复合概率定义的。这个动态系统是在一个抽象空间--主体行动的空间--用路径积分的形式描述的，非常类似于统计物理学或量子力学系统。我们证明，这种描述应用于Agent的行为空间，在简单情况下可归结为通常的优化结果。与标准优化相比，这样的描述显着地简化了对含有少量代理的系统的处理。然而，对于大量的代理来说，它变得毫无用处。因此，在第二步中，我们表明，对于大量的智能体，前面的描述等效于场论的更紧凑的描述。这就产生了对该系统的解析式近似处理。这种场论并不是通常意义上的微观经济系统的集合模型。它描述了一个由大量交互代理组成的环境。从这种描述中，可以检索出各种阶段或平衡，以及个体主体的行为及其与环境的相互作用。为了说明目的，本文研究了一个具有大量代理人的商业周期模型。
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英文标题：
《A Path Integral Approach to Business Cycle Models with Large Number of
  Agents》
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作者：
A\"ileen Lotz, Pierre Gosselin (IF), Marc Wambst (IRMA)
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最新提交年份：
2018
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分类信息：

一级分类：Economics        经济学
二级分类：General Economics        一般经济学
分类描述：General methodological, applied, and empirical contributions to economics.
对经济学的一般方法、应用和经验贡献。
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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：Economics        经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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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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英文摘要：
  This paper presents an analytical treatment of economic systems with an arbitrary number of agents that keeps track of the systems' interactions and agents' complexity. This formalism does not seek to aggregate agents. It rather replaces the standard optimization approach by a probabilistic description of both the entire system and agents'behaviors. This is done in two distinct steps. A first step considers an interacting system involving an arbitrary number of agents, where each agent's utility function is subject to unpredictable shocks. In such a setting, individual optimization problems need not be resolved. Each agent is described by a time-dependent probability distribution centered around his utility optimum. The entire system of agents is thus defined by a composite probability depending on time, agents' interactions and forward-looking behaviors. This dynamic system is described by a path integral formalism in an abstract space-the space of the agents' actions-and is very similar to a statistical physics or quantum mechanics system. We show that this description, applied to the space of agents'actions, reduces to the usual optimization results in simple cases. Compared to a standard optimization, such a description markedly eases the treatment of systems with small number of agents. It becomes however useless for a large number of agents. In a second step therefore, we show that for a large number of agents, the previous description is equivalent to a more compact description in terms of field theory. This yields an analytical though approximate treatment of the system. This field theory does not model the aggregation of a microeconomic system in the usual sense. It rather describes an environment of a large number of interacting agents. From this description, various phases or equilibria may be retrieved, along with individual agents' behaviors and their interactions with the environment. For illustrative purposes, this paper studies a Business Cycle model with a large number of agents.
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PDF链接：
https://arxiv.org/pdf/1810.07178