Mathematical finance is one of the most active areas of research, involving researchers from finance, mathematics, and statistics. This book presents an intermediate-level introduction to this important area.

This book explores the mathematics that underpins pricing models for derivative securities such as options, futures and swaps in modern markets. Models built upon the famous Black-Scholes theory require sophisticated mathematical tools drawn from modern stochastic calculus. However, many of the underlying ideas can be explained more simply within a discrete-time framework. This is developed extensively in this substantially revised second edition to motivate the technically more demanding continuous-time theory.

Pricing by Arbitrage * Martingale Measures * The Fundamental Theorem of Asset Pricing * Complete Markets and Martingale Representation * Stopping Times and American Options * A Review of Continuous Time Stochastic Calculus * European Options in Continuous Time * The American Option * Bonds and Term Structure * Consumption-Investment Strategies *