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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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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中文摘要：
在科学领域，尤其是在经济学领域，基于agent的建模已经成为一种广泛使用的建模方法。这些模型通常表示为一个大型差分方程组。在本研究中，我们从两个方面讨论了基于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。我们推导了这两个模型的时间连续公式，并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，我们证明了原始模型中所需的约束对于时间连续模型的稳定性不是必需的。结果表明，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，这种半隐式离散化的计算成本与原始模型相当。此外，我们还讨论了基于时间连续代理的计算经济市场模型的可能概率描述。特别是，我们提出了动力学理论的潜在优势，以推导基于agent模型的介观描述。举例来说，我们给出了Levy-Levy-Solomon和Franke-Westerhoff模型的两种概率描述。
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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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