NO-ARBITRAGE SYMMETRIES

doi:10.1007/s10473-022-0407-2

Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (4): 1373-1402.doi: 10.1007/s10473-022-0407-2

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NO-ARBITRAGE SYMMETRIES

Iván DEGANO¹, Sebastián FERRANDO², Alfredo GONZÁLEZ³

1. Departamento de Matemática. Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, CONICET, Funes 3350, Mar del Plata, 7600, Argentina;
2. Department of Mathematics, Ryerson University, 350 Victoria St., Toronto, Ontario, M5B 2K3, Canada;
3. Departamento de Matemática. Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, Mar del Plata, 7600, Argentina

Received:2020-09-18 Revised:2021-04-26 Online:2022-08-25 Published:2022-08-23
Contact: Sebastián FERRANDO,E-mail:ferrando@ryerson.ca E-mail:ferrando@ryerson.ca
Supported by:
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].

Abstract

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.

Key words: No arbitrage symmetry, convexity preserving maps, non-probabilistic markets

CLC Number:

91B24

Iván DEGANO, Sebastián FERRANDO, Alfredo GONZÁLEZ. NO-ARBITRAGE SYMMETRIES[J].Acta mathematica scientia,Series B, 2022, 42(4): 1373-1402.

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NO-ARBITRAGE SYMMETRIES

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