A Non-equilibrium Geometric No-arbitrage Principle

Wanxiao Tang () and Peibiao Zhao ()
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Wanxiao Tang: Nanjing University of Science and Technology
Peibiao Zhao: Nanjing University of Science and Technology

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 3, 1-15

Abstract: Abstract The present paper gets a novel and intimate correspondence between martingale in finances and one-parameter transform group in mathematics. This article confirms a criteria of the no-arbitrage problem in a frictionless financial market and a frictional financial market under the conformal transformation via this correspondence. The geometric no-arbitrage principle posed here also reveals a pricing principle on manifolds.

Keywords: Non-equilibrium; No-arbitrage; One-parameter transform group; Conformal transformation; 91B60; 91B28; 58C50; 51H25 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11009-023-10049-8

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