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. The reader progresses from a solid grounding in multi-variable calculus through a derivation of the Black–Scholes equation, its solution, properties, and applications.
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 PricesHedgingOptimizing PortfoliosAmerican Options
Readership: Undergraduate students in economics, finance and applied mathematics; professionals in banking, insurance and finance.