2017/09/21 by Daniel Q. Naiman, Edward R. Scheinerman, Naiman, Daniel Q. +1
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Economic theories and models #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1709.07446
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.