## 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.

#### Recommended Citation

Mason, Bradley A., "Tropical Algebra, Graph Theory, & Foreign Exchange Arbitrage" (2016). *Senior Honors Projects, 2010-current*. 349.

http://commons.lib.jmu.edu/honors201019/349