Arbitrage and Geometry

Daniel Q. Naiman; Edward R. Scheinerman

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arXiv · 1709.07446

Arbitrage and Geometry

Daniel Q. Naiman·Edward R. Scheinerman

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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.

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Daniel Q. Naiman, Edward R. Scheinerman. 2017-09-21. Arbitrage and Geometry. https://arxiv.org/abs/1709.07446

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