Title: Arbitrage and Geometry,
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.