Introduces Ito calculus, concentrating on applications in financial mathematics. Builds the standard diffusion type security market model, then treats the pricing of options in detail, introducing the method of option pricing via replication and no arbitrage. Presents a method of pricing options with partial differential equations, and presents examples of exotic options. Describes basics of Monte Carlo methods, tree methods, and finite difference methods, and deals with the martingale method and the stochastic control method for portfolio optimization. Assumes a previous basic course in probability theory. Author information is not given. Annotation c. Book News, Inc., Portland, OR (booknews.com)