Since the appearance of seminal works by R. Merton, and F. Black and M. Scholes, shastic processes have assumed an increasingly important role in the development of the mathematical theory of finance. This work examines, in some detail, that part of shastic finance pertaining to option pricing theory. Thus the exposition is confined to areas of shastic finance that are relevant to the theory, omitting such topics as futures and term-structure. This self-contained work begins with five introductory chapters on shastic analysis, making it accessible to readers with little or no prior knowledge of shastic processes or shastic analysis. These chapters cover the essentials of Ito's theory of shastic integration, integration with respect to semimartingales, Girsanov's Theorem, and a brief introduction to shastic differential equations. Subsequent chapters treat more specialized topics, including option pricing in discrete time, continuous time trading, arbitrage, complete markets, European options (Black and Scholes Theory), American options, Russian options, discrete approximations, and asset pricing with shastic volatility. In several chapters, new results are presented. A unique feature of the book is its emphasis on arbitrage, in particular, the relationship between arbitrage and equivalent martingale measures (EMM), and the derivation of necessary and sufficient conditions for no arbitrage (NA). {\it Introduction to Option Pricing Theory} is intended for students and researchers in statistics, applied mathematics, business, or economics, who have a background in measure theory and have completed probability theory at the intermediate level. The work lends itself to self-study, as well as to a one-semester course at the graduate level.
