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J. Risk Financial Manag. 2019, 12(1), 26; https://doi.org/10.3390/jrfm12010026

Geometric No-Arbitrage Analysis in the Dynamic Financial Market with Transaction Costs

,
and
*,†
Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 16 December 2018 / Revised: 17 January 2019 / Accepted: 1 February 2019 / Published: 6 February 2019
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Abstract

The present paper considers a class of financial market with transaction costs and constructs a geometric no-arbitrage analysis frame. Then, this paper arrives at the fact that this financial market is of no-arbitrage if and only if the curvature 2-form of a specific connection is zero. Furthermore, this paper derives the fact that the no-arbitrage condition for the one-period financial market is equivalent to the geometric no-arbitrage condition. Finally, an example states the equivalence between the geometric no-arbitrage condition and the existence of the solutions for a maximization problem of expected utility. View Full-Text
Keywords: geometric no-arbitrage; transaction cost; bid-ask spread geometric no-arbitrage; transaction cost; bid-ask spread
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Tang, W.; Zhao, J.; Zhao, P. Geometric No-Arbitrage Analysis in the Dynamic Financial Market with Transaction Costs. J. Risk Financial Manag. 2019, 12, 26.

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