An introduction to mathematical finance. (English) Zbl 0944.91024

Ross, Sheldon M.

Cambridge: Cambridge University Press. xv, 184 p. (1999).

This book provides an excellent introduction to the mathematics of finance. It is very well written, each new topic is clearly presented with plenty of examples and exercises. Little or no background material is required. The author covers basic probability as well as the rudiments of finance. The need for stochastic calculus is avoided by approximating geometric Brownian motion by an \(n\)-period binomial model, and then using the arbitrage theorem the Black-Scholes option pricing formula is derived. The author also looks at other approaches to pricing derivatives, for example Monte Carlo simulation to deal with exotic options. The later chapters deal with the limitations of the geometric Brownian motion model and alternative models are explored.
This book is very useful as a text for an introductory course in financial mathematics.

Reviewer: Julann O’Shea (Kildare)

MSC:

91-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to game theory, economics, and finance
91Gxx	Actuarial science and mathematical finance
60F05	Central limit and other weak theorems
60J65	Brownian motion

Keywords:

option pricing; arbitrage theorem; Black-Scholes option pricing formula; Monte Carlo simulation; exotic options; geometric Brownian motion model