经济网络中均衡与风险的局部弱极限
Local Weak Limits for Equilibrium and Risk in Economic Networks
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中文总结 AI 辅助
针对大型稀疏经济网络，提出基于局部弱收敛的局部计算方法，近似均衡分布并推广到风险度量，数值实验验证其准确性与高效性。
中文摘要 AI 辅助
我们研究了具有异质响应、冲击和双边风险暴露的大型稀疏经济网络中的均衡与风险评估。我们的方法通过在极限根网络上进行局部计算来近似均衡结果的分布。在标记的局部弱收敛下，我们证明了在两种情形下经验均衡分布在概率意义下的收敛性：一致压缩响应和有界单调非扩张响应（其下根迭代与上根迭代最终一致）。在后一种情形下，极限与可测的有限网络均衡选择无关，即使均衡不唯一。在有界定义域和连续性假设下，这种收敛性扩展到法律不变的风险度量，包括条件风险价值，并在额外正则性下给出递归深度误差界。在生产网络和支付清算系统上的数值实验说明了局部近似的准确性和计算优势。
英文摘要
We study equilibrium and risk evaluation in large sparse economic networks with heterogeneous responses, shocks, and bilateral exposures. Our approach approximates the distribution of equilibrium outcomes through local computations on a limiting rooted network. Under marked local weak convergence, we prove convergence in probability of the empirical equilibrium distribution in two settings: uniformly contractive responses and bounded monotone nonexpansive responses whose lower and upper root iterations coalesce. In the latter setting, the limit is independent of the measurable finite-network equilibrium selection, even when equilibria are not unique. Under bounded domain and continuity assumptions, this convergence extends to law-invariant risk measures, including conditional value-at-risk, with recursion-depth error bounds under additional regularity. Numerical experiments on production networks and payment clearing systems illustrate the accuracy and computational benefits of the local approximation.
发表机构
- University of Florida（佛罗里达大学）
机构由 AI 辅助整理，请以论文原文为准。
