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Dec 19, 2025
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MATH 4580 - Elements of Financial Mathematics
This course is designed for advanced undergraduate students and master’s degree students interested in applications of mathematics in finance. The course introduces basic ideas and methods of stochastic calculus and applications of these methods to financial models, particularly to the pricing and hedging of derivative securities in continuous time models. The course covers the following topics: introduction to financial derivatives, concepts of arbitrage and risk-neutral pricing, probability distribution, expectation, conditional expectation, Brownian motion, Itô’s integral, Itô’s formula and its applications to financial modeling, and also the Black-Scholes option pricing model.
Requisites: MATH 3500
Credit Hours: 3
Repeat/Retake Information: May be retaken two times excluding withdrawals, but only last course taken counts.
Lecture/Lab Hours: 3.0 lecture
Grades: Eligible Grades: A-F,WP,WF,WN,FN,AU,I
Learning Outcomes: - Students will be able to describe standard terminology of mathematical finance such as: options, arbitrage, risk-neutral pricing and hedging.
- Students will be able to describe and analyze elements of the theory of stochastic calculus and stochastic processes, with the emphasis on Brownian motion, Itô’s integral, Itô’s formula and their applications.
- Students will be able to use various analytical and probabilistic techniques to study stochastic models that appear in financial applications.
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