As the total value of the global financial market outgrew the value of the real economy, financial institutions created a global web of interactions that embodies systemic risks. Understanding these networks requires new theoretical approaches and new tools for quantitative analysis. Statistical physics contributed significantly to this challenge by developing new metrics and models for the study of financial network structure, dynamics, and stability and instability. In this Review, we introduce network representations originating from different financial relationships, including direct interactions such as loans, similarities such as co-ownership and higher-order relations such as contracts involving several parties (for example, credit default swaps) or multilayer connections (possibly extending to the real economy). We then review models of financial contagion capturing the diffusion and impact of shocks across each of these systems. We also discuss different notions of ‘equilibrium’ in economics and statistical physics, and how they lead to maximum entropy ensembles of graphs, providing tools for financial network inference and the identification of early-warning signals of system-wide instabilities.

随着全球金融市场的总价值超过实体经济的价值，金融机构创建了一个包含系统性风险的全球互动网络。理解这些网络需要新的理论方法和新的定量分析工具。统计物理学通过开发用于研究金融网络结构、动力学以及稳定性和不稳定性的新指标和模型，为这一挑战做出了重大贡献。在这篇综述中，我们介绍了源自不同金融关系的网络表示，包括直接交互（如贷款）、相似性（如共同所有权）和高阶关系（如涉及多方的合同（例如，信用违约掉期）或多层连接）。可能延伸到实体经济）。然后，我们回顾了捕捉冲击在每个系统中的扩散和影响的金融传染模型。我们还讨论了经济学和统计物理学中“均衡”的不同概念，以及它们如何导致图的最大熵集合，为金融网络推理和识别系统范围不稳定性的早期预警信号提供工具。