AI 中文总结
研究度量状态空间上货币风险度量理论，以在参考状态消失的利普希茨函数空间为金融头寸定义域，因定义域特性标准方法不适用，通过沿基准偏差工具使用加性推导对偶表示，涵盖多种风险。
AI 中文摘要
本文发展了度量状态空间上货币风险度量的理论。我们提出在参考状态消失的利普希茨函数空间作为金融头寸的自然定义域。相关的无利普希茨空间提供了其规范预对偶，将锚定的利普希茨收益与解释为围绕基准的质量重新分布的基于运输的对偶变量联系起来。由于该定义域缺乏常数且在利普希茨范数下不必是巴拿赫格，标准现金加性方法不直接适用。我们通过沿基准偏差工具使用加性来解决此问题，并推导凸和相干风险度量的对偶表示。该框架涵盖时间现金流、路径依赖收益、网络风险和模型不确定性。
英文摘要
This paper develops a theory of monetary risk measures on metric state spaces. We propose the space of Lipschitz functions vanishing at a reference state as a natural domain for financial positions. The associated Lipschitz-free space provides its canonical predual, linking anchored Lipschitz payoffs to transport-based dual variables interpreted as redistributions of mass around the benchmark. Since the domain lacks constants and need not be a Banach lattice under the Lipschitz norm, standard cash-additive methods do not apply directly. We address this by using additivity along benchmark-deviation instruments and derive dual representations for convex and coherent risk measures. The framework covers temporal cash flows, path-dependent payoffs, network risk, and model uncertainty.
Comments23 pages. Submitted for publication
