TY - BOOK AU - Williams, J.R. TI - Introduction to the mathematics of finance SN - 9780821868829 U1 - HF5691 PY - 2011/// PB - AMS N1 - Chapter 1. Financial markets and derivatives Chapter 2. Binomial model Chapter 3. Finite market model Chapter 4. Black-Scholes model Chapter 5. Multi-dimensional Black-Scholes model Appendix A. Conditional expectation and Lp -spaces Appendix B. Discrete time stochastic processes Appendix C. Continuous time stochastic processes Appendix D. Brownian motion and stochastic integration N2 - The book begins with the development of the basic ideas of hedging and pricing of European and American derivatives in the discrete (i.e., discrete time and discrete state) setting of binomial tree models. Then a general discrete finite market model is introduced, and the fundamental theorems of asset pricing are proved in this setting. Tools from probability such as conditional expectation, filtration, (super)martingale, equivalent martingale measure, and martingale representation are all used first in this simple discrete framework. This provides a bridge to the continuous (time and state) setting, which requires the additional concepts of Brownian motion and stochastic calculus. The simplest model in the continuous setting is the famous Black-Scholes model, for which pricing and hedging of European and American derivatives are developed. The book concludes with a description of the fundamental theorems for a continuous market model that generalizes the simple Black-Scholes model in several directions ER -