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This book presents a self-contained, comprehensive, and yet concise and condensed overview of the theory and methods of probability, integration, stochastic processes, optimal control, and their connections to the principles of asset pricing. The book is broader in scope than other introductory-level graduate texts on the subject, requires fewer prerequisites, and covers the relevant material at greater depth, mainly without rigorous technical proofs. The book brings to an introductory level certain concepts and topics that are usually found in advanced research monographs on stochastic processes and asset pricing, and it attempts to establish greater clarity on the connections between these two fields.

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"In this ambitious book, the author guides a dedicated reader from elementary probability to the advanced stochastic analysis of modern mathematical finance, with rewarding excursions into topics seldom seen in introductory texts." - Paul Glasserman, Jack R. Anderson Professor of Business, Columbia University

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Andrew Lyasoff is affiliated with the Mathematical Finance Program at Boston Universitys Questrom School of Business.

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