Arbitrage Concepts Under Trading Restrictions in Discrete-Time Financial Markets
29 Pages Posted: 21 Jul 2020 Last revised: 20 Feb 2021
Date Written: September 19, 2020
In a discrete-time setting, we study arbitrage concepts in the presence of convex trading constraints. We show that solvability of portfolio optimization problems is equivalent to absence of arbitrage of the first kind, a condition weaker than classical absence of arbitrage opportunities. We center our analysis on this characterization of market viability and derive versions of the fundamental theorems of asset pricing based on portfolio optimization arguments. By considering specifically a discrete-time setup, we simplify existing results and proofs that rely on semimartingale theory, thus allowing for a clear understanding of the foundational economic concepts involved. We exemplify these concepts, as well as some unexpected situations, in the context of one-period factor models with arbitrage opportunities under borrowing constraints.
Keywords: Trading constraints, market viability, arbitrage of the first kind, numeraire portfolio
JEL Classification: C02, C61, G11, G12
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