Arbitrage Concepts Under Trading Restrictions in Discrete-Time Financial Markets

29 Pages Posted: 21 Jul 2020 Last revised: 20 Feb 2021

See all articles by Claudio Fontana

Claudio Fontana

University of Padova, Department of Mathematics

Wolfgang J. Runggaldier

University of Padova, Department of Mathematics

Date Written: September 19, 2020

Abstract

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

Suggested Citation

Fontana, Claudio and Runggaldier, Wolfgang J., Arbitrage Concepts Under Trading Restrictions in Discrete-Time Financial Markets (September 19, 2020). Journal of Mathematical Economics, Vol. 92, 2021, Available at SSRN: https://ssrn.com/abstract=3637373 or http://dx.doi.org/10.2139/ssrn.3637373

Claudio Fontana (Contact Author)

University of Padova, Department of Mathematics ( email )

Via Trieste 63
Padova, 35121
Italy

Wolfgang J. Runggaldier

University of Padova, Department of Mathematics ( email )

Via Trieste, 63
Padova, 35121
Italy
+39 049 827 1454 (Phone)

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