Abstract

This book offers a unified treatment of selected topics in the theory of financial markets. Starting with discrete time models, Dothan introduces discrete time stochastic calculus and discrete martingale methods of intuitive simplicity to characterize attainability, completeness, pricing, and the relationship between risk and return in financial markets. Subsequently, he uses the intuition developed in conjunction with the discrete time theory to introduce continuous time calculus for continuous, jump, and mixed continuous-jump processes, and to deal with attainability, completeness, pricing, and the relationship between risk and return in general continuous time models. Throughout, the exposition of the continuous time theory emphasizes the analogies between discrete time and continuous time methods and results. The book includes many examples, applications to the pricing of options and other derivative securities, and an extensive discussion of the Black-Scholes model and its most general theoretical extension.