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

Wanxiao Tang, Jun Zhao and Peibiao Zhao
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Wanxiao Tang: Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China
Jun Zhao: Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China
Peibiao Zhao: Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China

JRFM, 2019, vol. 12, issue 1, 1-17

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.

Keywords: geometric no-arbitrage; transaction cost; bid-ask spread (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2019
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