09-23-2026, 08:29 PM
Mathematics and Tools for Financial Engineering by Petros A. Ioannou is a textbook that builds the mathematical foundations needed to understand financial engineering. The first half develops essential tools including set theory, linear algebra, sequences and series, real analysis, numerical approximation, optimization, Lagrange multipliers, probability, and stochastic processes. The book emphasizes both mathematical understanding and practical engineering techniques, using examples and problems to connect abstract concepts with financial applications.
The second half applies these tools to financial problems, covering interest rates and the time value of money, bonds, dynamic models of financial assets, portfolio optimization, option pricing, the Black–Scholes framework, the “Greeks,” and hedging. A recurring theme is the use of mathematical and computational models to represent uncertainty and support financial analysis—for example, stochastic processes for asset prices and optimization methods for balancing portfolio risk and return.
The book is aimed primarily at advanced undergraduates and graduate students in finance or financial engineering, but it can also serve as an introduction to the mathematical techniques used in numerical analysis, modeling, optimization, and data science.
BOOK
The second half applies these tools to financial problems, covering interest rates and the time value of money, bonds, dynamic models of financial assets, portfolio optimization, option pricing, the Black–Scholes framework, the “Greeks,” and hedging. A recurring theme is the use of mathematical and computational models to represent uncertainty and support financial analysis—for example, stochastic processes for asset prices and optimization methods for balancing portfolio risk and return.
The book is aimed primarily at advanced undergraduates and graduate students in finance or financial engineering, but it can also serve as an introduction to the mathematical techniques used in numerical analysis, modeling, optimization, and data science.
BOOK
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