Universal Approximation Theorems for Spectral Decision Functionals
Mathematics verified. Core theorems are machine-checked in Lean 4.
Prose and presentation may not have been human-reviewed.
Abstract
We prove universal approximation results for a broad class of decision functionals represented in spectral coordinates. The theorem characterizes expressivity in terms of basis regularity, coefficient decay, and functional smoothness, and provides quantitative approximation rates. This establishes a common approximation backbone for risk, allocation, and control functionals.
Length
1,926 words
Claims
4 theorems
Status
Draft
Novelty
Lifts classical CDF-level spectral (COS) approximation guarantees to the level of decision functionals (risk measures, pricing maps, allocation rules) via Lipschitz transfer, giving explicit rates rather than mere density results.