No-Arbitrage Symmetries
Mathematical Finance
2020-08-17 v1
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. 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
Cite
@article{arxiv.2008.06184,
title = {No-Arbitrage Symmetries},
author = {I. L. Degano and S. E. Ferrando and A. L. Gonzalez},
journal= {arXiv preprint arXiv:2008.06184},
year = {2020}
}
Comments
35 pages