Mathematics of Finance

Donald G. Saari is Emeritus Professor of Mathematics and Economics at the University of California, Irvine. His contributions to voting theory, economics, and celestial mechanics are widely celebrated, and his achievements include election to the U.S. National Academy of Sciences and the Chauvenet Prize for mathematical exposition. His books Geometry of Voting and Basic Geometry of Voting are celebrated for their seminal contributions to mathematical voting theory.

• 1. Preliminaries via Gambles.- 2. Options.- 3. Modeling.- 4. Some Probability.- 5. The Black–Scholes Equation.- 6. Solutions of Black–Scholes.- 7. Partial information: the Greeks.- 8. Sketching and the American Options.- 9. Embellishments.

“This textbook provides excellent tools for a holistic understanding of mathematical finance, which combine intuitive common sense with financial and mathematical concepts. The book appeared as notes for undergraduates from a variety of backgrounds, from mathematics and computer science to economics and finance.” (Nikita Y. Ratanov, Mathematical Reviews, August, 2020)