2020/08/14 by Iván Degano, Degano, I. L., Sebastián Ferrando +3
Economics, Econometrics and Finance · Mathematics · #Economic theories and models #FOS: Economics and business #Mathematical Finance (q-fin.MF) #Mathematical and Theoretical Analysis #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2008.06184
openalex publication_date 2020/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. The 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 in a detailed example. Our context makes the result available to the stochastic setting as a special case