Path-Space Model Risk via Signature-Induced Optimal Transport
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.