Senior Honors Projects, 2010-current

Date of Award

Spring 2016

Document Type

Thesis

Degree Name

Bachelor of Science (BS)

Department

Department of Mathematics and Statistics

Advisor(s)

Edwin O'Shea, Ph.D.

Abstract

We answer the question, given n currencies and k trades, how can a maximal arbitrage opportunity be found and what is its value? To answer this question, we use techniques from graph theory and employ a max-plus algebra (commonly known as tropical algebra). Further, we show how the tropical eigenvalue of a foreign exchange rate matrix relates to arbitrage among the currencies and can be found algorithmically. We finish by employing time series techniques to study the stability of maximal, high-currency arbitrage opportunities.

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