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.
"This book is lucid....The author should be highly commended for his efforts.....A very good introduction to the modern theory of financial markets. I will certainly recommend it very highly to students and researchers of modern financial economics."--The Journal of Finance
"This books provides a 'unified treatment of selected topics in the theory of financial markets' and an 'introduction to the mathematics of this theory'....A useful supplement to existing texts for teaching basic concepts of information structures, budget sets, arbitrage, etc."--The Review of Financial Studies
"Well done!"--Darrell Duffie, Stanford University
"A good survey of financial markets, quite exhaustive, with some new results. A clear presentation of probabilistic tools is given. The book is in an agreeable format and very pleasant to read." --Mathematical Reviews