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摘要翻译：
在科学领域，特别是在经济学领域，基于Agent的建模已经成为一种广泛应用的建模方法。这些模型通常被表述为一个大的差分方程组。在本研究中，我们讨论了两个基于Agent的计算经济市场模型：Levy-Levy-Solomon模型和Franke-Westerhoff模型的数值建模和概率描述。我们导出了这两个模型的时间连续公式，特别讨论了时间尺度对Levy-Levy-Solomon模型行为的影响。对于Franke-Westerhoff模型，我们证明了原模型中所要求的约束对于时间连续模型的稳定性是不必要的。证明了时间连续系统的半隐式离散化保持了这种无条件稳定性。此外，这种半隐式离散化可以以与原始模型相当的代价计算。此外，我们讨论了时间连续的基于Agent的计算经济市场模型的可能的概率描述。特别是，我们提出了动力学理论的潜在优势，以导出基于Agent的模型的介观特征。举例说明了Levy-Levy-Solomon模型和Franke-Westerhoff模型的两种概率描述。
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英文标题：
《Robust Mathematical Formulation and Probabilistic Description of
Agent-Based Computational Economic Market Models》
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作者：
Maximilian Beikirch, Simon Cramer, Martin Frank, Philipp Otte, Emma
Pabich, Torsten Trimborn
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最新提交年份：
2021
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Trading and Market Microstructure 交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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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：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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一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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英文摘要：
In science and especially in economics, agent-based modeling has become a widely used modeling approach. These models are often formulated as a large system of difference equations. In this study, we discuss two aspects, numerical modeling and the probabilistic description for two agent-based computational economic market models: the Levy-Levy-Solomon model and the Franke-Westerhoff model. We derive time-continuous formulations of both models, and in particular we discuss the impact of the time-scaling on the model behavior for the Levy-Levy-Solomon model. For the Franke-Westerhoff model, we proof that a constraint required in the original model is not necessary for stability of the time-continuous model. It is shown that a semi-implicit discretization of the time-continuous system preserves this unconditional stability. In addition, this semi-implicit discretization can be computed at cost comparable to the original model. Furthermore, we discuss possible probabilistic descriptions of time continuous agent-based computational economic market models. Especially, we present the potential advantages of kinetic theory in order to derive mesoscopic desciptions of agent-based models. Exemplified, we show two probabilistic descriptions of the Levy-Levy-Solomon and Franke-Westerhoff model.
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PDF链接：
https://arxiv.org/pdf/1904.04951
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