Nonlinear taxation and bounded arbitrage

Abstract

We provide a complete characterization of arbitrage in securities markets with nonlinear taxation. Using a relative pricing framework, we analyze a multi-period market with a convex tax function and identify conditions under which arbitrage arises. Our results distinguish between bounded and unbounded arbitrage opportunities, depending on the interaction between the shape of the tax function and an endogenous equilibrium tax rate. Extending Ross (1987), we prove that a single-period market with nonlinear taxation is always arbitrage-free. Our work illustrates how stochastic convex optimization can be applied to analyze the effects of market frictions in a relative pricing setting. All results are constructive and yield closed-form expressions for arbitrage gains.

Keywords: bounded arbitrage, nonlinear taxation, arbitrage theory, relative pricing, convex optimization, stochastic optimization, market frictions

JEL Classification: C61, D53, G12, H24