用格点ϕ⁴场论模拟金融市场的多主体系统，再现收益厚尾和波动聚集现象。
Lattice $ϕ^{4}$ field theory as a multi-agent system of financial markets
- 将每个格点视为受竞争作用影响的交易主体，模仿邻居或跟随多数/少数意见。
- 数值验证显示模型能复现伦敦证券交易所FTSE 100指数的真实市场特征。
- 连续自由度带来更强表征能力，优于基于伊辛模型的多主体系统。
我们引入具有挫折动力学的ϕ⁴格点场论作为多主体系统，以重现金融市场的典型特征，如收益的厚尾分布和波动聚集。每个格点对应一个连续自由度的主体，其买卖决策受多重竞争作用影响：包括促进模仿邻近主体的协作项，以及强制主体服从多数或少数意见的虚构场。通过马尔可夫场结构对ϕ⁴概率分布进行构造性分解，并结合Ferrenberg-Swendsen接受/拒绝采样步骤重构系统。数值实验表明，该多主体ϕ⁴场论能有效复现伦敦证券交易所FTSE 100指数的实证行为特征。最后讨论指出，ϕ⁴格点场论中连续自由度的存在，使其在表征能力上超越基于伊辛模型构建的多主体系统。
原文摘要 · Abstract (English)
We introduce a $ϕ^{4}$ lattice field theory with frustrated dynamics as a multi-agent system to reproduce stylized facts of financial markets such as fat-tailed distributions of returns and clustered volatility. Each lattice site, represented by a continuous degree of freedom, corresponds to an agent experiencing a set of competing interactions which influence its decision to buy or sell a given stock. These interactions comprise a cooperative term, which signifies that the agent should imitate the behavior of its neighbors, and a fictitious field, which compels the agent instead to conform with the opinion of the majority or the minority. To introduce the competing dynamics we exploit the Markov field structure to pursue a constructive decomposition of the $ϕ^{4}$ probability distribution which we recompose with a Ferrenberg-Swendsen acceptance or rejection sampling step. We then verify numerically that the multi-agent $ϕ^{4}$ field theory produces behavior observed on empirical data from the FTSE 100 London Stock Exchange index. We conclude by discussing how the presence of continuous degrees of freedom within the $ϕ^{4}$ lattice field theory enables a representational capacity beyond that possible with multi-agent systems derived from Ising models.
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