Abstract
The no-arbitrage property is widely accepted to be a centerpiece of modern financial mathematics and could be considered to be a financial law applicable to a large class of (idealized) markets. This paper addresses the following basic question: can one characterize the class of transformations that leave the law of no-arbitrage invariant? We provide a geometric formalization of this question in a non probabilistic setting of discrete time-the so-called trajectorial models. The paper then characterizes, in a local sense, the no-arbitrage symmetries and illustrates their meaning with a detailed example. Our context makes the result available to the stochastic setting as a special case.
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The research of S.E. Ferrando is supported in part by an NSERC grant. The research of I.L. Degano and A.L. González is supported in part by the National University of Mar del Plata, Argentina [EXA902/18].
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Degano, I., Ferrando, S. & González, A. No-Arbitrage Symmetries. Acta Math Sci 42, 1373–1402 (2022). https://doi.org/10.1007/s10473-022-0407-2
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DOI: https://doi.org/10.1007/s10473-022-0407-2