Arbitrage and Geometry
Mathematical Finance
2017-09-25 v1 Statistics Theory
Statistics Theory
Abstract
This article introduces the notion of arbitrage for a situation involving a collection of investments and a payoff matrix describing the return to an investor of each investment under each of a set of possible scenarios. We explain the Arbitrage Theorem, discuss its geometric meaning, and show its equivalence to Farkas' Lemma. We then ask a seemingly innocent question: given a random payoff matrix, what is the probability of an arbitrage opportunity? This question leads to some interesting geometry involving hyperplane arrangements and related topics.
Cite
@article{arxiv.1709.07446,
title = {Arbitrage and Geometry},
author = {Daniel Q. Naiman and Edward R. Scheinerman},
journal= {arXiv preprint arXiv:1709.07446},
year = {2017}
}
Comments
22 pages, 9 figures