Robust No Arbitrage and the Solvability of Vector-Valued Utility Maximization Problems

9 Pages Posted: 6 Sep 2019

See all articles by Andreas Hamel

Andreas Hamel

Free University of Bozen-Bolzano

Birgit Rudloff

Vienna University of Economics and Business

Zhou Zhou

The University of Sydney

Date Written: August 21, 2019

Abstract

A market model with d assets in discrete time is considered where trades are subject to proportional transaction costs given via bid-ask spreads, while the existence of a numeraire is not assumed. It is shown that robust no arbitrage holds if, and only if, there exists a Pareto solution for some vector-valued utility maximization problem with component-wise utility functions. Moreover, it is demonstrated that a consistent price process can be constructed from the Pareto maximizer.

Keywords: Bid-ask spread, robust no arbitrage, Pareto maximizer, utility maximization, consistent price process

Suggested Citation

Hamel, Andreas and Rudloff, Birgit and Zhou, Zhou, Robust No Arbitrage and the Solvability of Vector-Valued Utility Maximization Problems (August 21, 2019). Available at SSRN: https://ssrn.com/abstract=3445278 or http://dx.doi.org/10.2139/ssrn.3445278

Andreas Hamel

Free University of Bozen-Bolzano ( email )

Sernesiplatz 1
Bozen-Bolzano, BZ 39100
Italy

Birgit Rudloff

Vienna University of Economics and Business ( email )

Welthandelsplatz 1
Vienna, Wien 1020
Austria

Zhou Zhou (Contact Author)

The University of Sydney ( email )

University of Sydney
Sydney, NSW 2006
Australia

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