On general financial markets with concave transactions costs

Agnieszka Rygiel; Lukasz Stettner

doi:10.3934/dcdsb.2025012

Article Contents

2025, Volume 30, Issue 11: 4462-4481. Doi: 10.3934/dcdsb.2025012

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On general financial markets with concave transactions costs

Agnieszka Rygiel^1, and
Lukasz Stettner^2, ,

1.
Kraków University of Economics, Department of Mathematics, Poland
2.
Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, 00-656 Warsaw, Poland

^*Corresponding author: Lukasz Stettner
^*Corresponding author: Lukasz Stettner

Received: September 2024

Revised: January 2025

Early access: February 9, 2025

Published online: February 9, 2025

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Abstract

In this paper, we study markets with concave transaction costs which depend in a concave way on the volume of transaction. This is a typical situation in the case of small investors, which commonly appears in currency and real estate markets. Sufficient conditions for absence of arbitrage are formulated. New notion of asymptotic arbitrage is introduced and used to study the above mentioned markets.

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Mathematics Subject Classification: Primary: 93E20, 91G15; Secondary: 91G10, 49J53.

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References

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