A Nonlinear Spectral Fundamental Theorem of Asset Pricing
Mathematics verified. Core theorems are machine-checked in Lean 4.
Prose and presentation may not have been human-reviewed.
Abstract
Classical FTAP characterizes no-arbitrage in linear pricing systems. We develop a nonlinear spectral extension in which state prices are represented as mode-dependent functionals over a spectral decomposition of market states. We prove equivalence between no-free-lunch conditions and existence of a consistent nonlinear spectral pricing kernel, yielding a unified theorem that nests CAPM-like linear cases as a strict special regime.
Length
1,654 words
Claims
4 theorems
Status
Draft
Novelty
Recasting FTAP in a spectral-mode basis so that each PCA mode carries its own convex pricing functional, unifying transaction-cost-style nonlinearities with no-arbitrage duality per mode.