An Undergraduate Introduction to Financial Mathematics

This textbook provides an introduction to financial mathematics and financial engineering for undergraduate students who have completed a three- or four-semester sequence of calculus courses. It introduces the theory of interest, discrete and continuous random variables and probability, stochastic processes, linear programming, the Fundamental Theorem of Finance, option pricing, hedging, and portfolio optimization. This third edition expands on the second by including a new chapter on the extensions of the Black-Scholes model of option pricing and a greater number of exercises at the end of each chapter. More background material and exercises added, with solutions provided to the other chapters, allowing the textbook to better stand alone as an introduction to financial mathematics. The reader progresses from a solid grounding in multivariable calculus through a derivation of the Black-Scholes equation, its solution, properties, and applications. The text attempts to be as self-contained as possible without relying on advanced mathematical and statistical topics. The material presented in this book will adequately prepare the reader for graduate-level study in mathematical finance.
Contents:The Theory of InterestDiscrete ProbabilityNormal Random Variables and ProbabilityThe Arbitrage TheoremRandom Walks and Brownian MotionForwards and FuturesOptionsSolution of the Black-Scholes EquationDerivatives of Black-Scholes Option PricesHedgingExtensions of the Black-Scholes ModelOptimizing PortfoliosAmerican Options
Readership: Undergraduate students in finance, economics, and applied mathematics; professionals in banking, insurance and finance.