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This book develops the theory of probability and mathematical statistics at a level suitable for those at the frontiers of applied research, and it provides the necessary concepts of measure theory and analysis along the way. Down-to-earth explanations and an abundance of examples and exercises throughout the text make these concepts accessible to those with preparation limited to vector calculus and elementary statistics. Complete, detailed solutions to all the exercises are at the end of each chapter. These both develop one's technique for problem solving and afford immediate...

This book presets techniques for valuing derivative securities at a level suitable for practitioners, students in doctoral programs in economics and finance, and those in masters-level programs in financial mathematics and computational finance. It provides the necessary mathematical tools from analysis, probability theory, the theory of stochastic processes, and stochastic calculus, making extensive use of examples. It also coveres pricing theory, with emphasis on martingale methods. The chapters are organized around the assumptions made about the dynamics of underlying price processes....