AI 中文总结
该研究针对路径空间模型风险，提出签名诱导的最优传输框架，通过环境特征空间松弛得出相关界和方法，可用于金融和保险的压力测试及模型误设问题，能有效控制校正预算。
AI 中文摘要
我们为路径空间模型风险提出了一个由签名诱导的最优传输框架，其中随机路径律之间的模糊性通过共同耦合下签名坐标上的最优传输成本进行分解。通过环境特征空间松弛，我们为仿射签名分数和仿射半空间事件推导出仅依赖于基线模型的显式稳健期望和概率界。在这两种情况下，校正由相同的有效预算控制，该预算仅取决于仿射分数和模糊集的预算向量。此外，相同的量导致了一种考虑预算的稀疏签名替代方法，用于更一般的、可能隐式的或数据驱动的路径泛函。我们通过金融和保险中的受控压力测试和基准模型误设问题来说明所得方法。
英文摘要
We propose a signature-induced, optimal transport framework for path-space model risk, in which ambiguity between stochastic path laws is factorized through optimal transport costs on signature coordinates under a common coupling. Via an ambient feature-space relaxation, we derive for affine signature scores and affine half-space events explicit robust expectation and probability bounds that depend only on the baseline model. In both cases, the correction is governed by the same effective budget, which depends only on the affine score and the budget vector of the ambiguity set. Moreover, the same quantity leads to a budget-aware sparse signature surrogate method for more general, possibly implicit, or data-driven, path functionals. We illustrate the resulting methodology through controlled stress tests and benchmark model-misspecification problems in finance and insurance.
Comments30 pages, 3 figures
