Introduction to Mathematical Finance: Discrete Time Models by Stanley R. Pliska

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This volume is designed to serve as a textbook for advanced undergraduate and beginning graduate students who seek a rigorous yet accessible introduction to the modern financial theory of security markets. Exercises are provided to check understanding and provide supplemental information.

FORMATHardcover LANGUAGEEnglish CONDITIONBrand New Publisher Description

The purpose of this book is to provide a rigorous yet accessible introduction to the modern financial theory of security markets. The main subjects are derivatives and portfolio management. The book is intended to be used as a text by advanced undergraduates and beginning graduate students. It is also likely to be useful to practicing financial engineers, portfolio manager, and actuaries who wish to acquire a fundamental understanding of financial theory. The book makes heavy use of mathematics, but not at an advanced level. Various mathematical concepts are developed as needed, and computational examples are emphasized.

Back Cover

This book is designed to serve as a textbook for advanced undergraduate and beginning graduate students who seek a rigorous yet accessible introduction to the modern financial theory of security markets. This is a subject that is taught in both business schools and mathematical science departments. The full theory of security markets requires knowledge of continuous time stochastic process models, measure theory, mathematical economics, and similar prerequisites which are generally not learned before the advanced graduate level. Hence a proper study of the full theory of security markets requires several years of graduate study. However, by restricting attention to discrete time models of security prices it is possible to acquire mathematics. In particular, while living in a discrete time world it is possible to learn virtually all of the important financial concepts. The purpose of this book is to provide such an introductory study.There is still a lot of mathematics in this book. The reader should be comfortable with calculus, linear algebra, and probability theory that is based on calculus, (but not necessarily measure theory). Random variables and expected values will be playing important roles. The book will develop important notions concerning discrete time stochastic processes; prior knowledge here will be useful but is not required. Presumably the reader will be interested in finance and thus will come with some rudimentary knowledge of stocks, bonds, options, and financial decision making. The last topic involves utility theory, of course; hopefully the reader will be familiar with this and related topics of introductory microeconomic theory. Some exposure to linear programming would be advantageous, but not necessary.The aim of this book is to provide a rigorous treatment of the financial theory while maintaining a casual style. Readers seeking institutional knowledge about securities, derivatives, and portfolio management should look elsewhere, but those seeking a careful introduction to financial engineering will find that this is a useful and comprehensive introduction to the subject.

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This book is designed to serve as a textbook for advanced undergraduate and beginning graduate students who seek a rigorous yet accessible introduction to the modern financial theory of security markets. This is a subject that is taught in both business schools and mathematical science departments. The full theory of security markets requires knowledge of continuous time stochastic process models, measure theory, mathematical economics, and similar prerequisites which are generally not learned before the advanced graduate level. Hence a proper study of the full theory of security markets requires several years of graduate study. However, by restricting attention to discrete time models of security prices it is possible to acquire mathematics. In particular, while living in a discrete time world it is possible to learn virtually all of the important financial concepts. The purpose of this book is to provide such an introductory study. There is still a lot of mathematics in this book. The reader should be comfortable with calculus, linear algebra, and probability theory that is based on calculus, (but not necessarily measure theory). Random variables and expected values will be playing important roles. The book will develop important notions concerning discrete time stochastic processes; prior knowledge here will be useful but is not required. Presumably the reader will be interested in finance and thus will come with some rudimentary knowledge of stocks, bonds, options, and financial decision making. The last topic involves utility theory, of course; hopefully the reader will be familiar with this and related topics of introductory microeconomic theory. Some exposure to linear programming would be advantageous, but not necessary. The aim of this book is to provide a rigorous treatment of the financial theory while maintaining a casual style. Readers seeking institutional knowledge about securities, derivatives, and portfolio management should look elsewhere, but those seeking a careful introduction to financial engineering will find that this is a useful and comprehensive introduction to the subject.

Author Biography

Stanley Pliska is the founding editor of the scholarly journal Mathematical Finance. He is noted for his fundamental research on the mathematical and economic theory of security prices, especially his development of important bridges between stochastic calculus and arbitrage pricing theory as well as his discovery of the risk neutral computational approach for portfolio optimization problems. He is currently teaching and researching in the areas of interest rate derivatives and dynamic asset allocation.

Table of Contents

Preface v Acknowledgments x 1 Single Period Securities Markets 1 2 Single Period Consumption and Investment 33 3 Multiperiod Securities Markets 72 4 Options, Futures, and Other Derivatives 112 5 Optimal Consumption and Investment Problems 149 6 Bonds and Interest Rate Derivatives 200 7 Models with Infinite Sample Spaces 238 Appendix: Linear Programming 250 Bibliography 254 Index 257

Review

"I believe that this is an excellent text for undergraduate or MBA classes on Mathematical Finance. The bulk of the book describes a model with finitely many, discrete trading dates, and a finite sample space, thus it avoids the technical difficulties associated with continuous time models. The major strength of this book is its careful balance of mathematical rigor and intuition." Peter Lakner, New York University

Long Description

This book is designed to serve as a textbook for advanced undergraduate and beginning graduate students who seek a rigorous yet accessible introduction to the modern financial theory of security markets. This is a subject that is taught in both business schools and mathematical science departments. The full theory of security markets requires knowledge of continuous time stochastic process models, measure theory, mathematical economics, and similar prerequisites which are generally not learned before the advanced graduate level. Hence a proper study of the full theory of security markets requires several years of graduate study. However, by restricting attention to discrete time models of security prices it is possible to acquire mathematics. In particular, while living in a discrete time world it is possible to learn virtually all of the important financial concepts. The purpose of this book is to provide such an introductory study. There is still a lot of mathematics in this book. The reader should be comfortable with calculus, linear algebra, and probability theory that is based on calculus, (but not necessarily measure theory). Random variables and expected values will be playing important roles. The book will develop important notions concerning discrete time stochastic processes; prior knowledge here will be useful but is not required. Presumably the reader will be interested in finance and thus will come with some rudimentary knowledge of stocks, bonds, options, and financial decision making. The last topic involves utility theory, of course; hopefully the reader will be familiar with this and related topics of introductory microeconomic theory. Some exposure to linear programming would be advantageous, but not necessary. The aim of this book is to provide a rigorous treatment of the financial theory while maintaining a casual style. Readers seeking institutional knowledge about securities, derivatives, and portfolio management should look elsewhere, but those seeking a careful introduction to financial engineering will find that this is a useful and comprehensive introduction to the subject.

Review Text

"I believe that this is an excellent text for undergraduate or MBA classes on Mathematical Finance. The bulk of the book describes a model with finitely many, discrete trading dates, and a finite sample space, thus it avoids the technical difficulties associated with continuous time models. The major strength of this book is its careful balance of mathematical rigor and intuition." Peter Lakner, New York University

Review Quote

"I believe that this is an excellent text for undergraduate or MBA classes on Mathematical Finance. The bulk of the book describes a model with finitely many, discrete trading dates, and a finite sample space, thus it avoids the technical difficulties associated with continuous time models. The major strength of this book is its careful balance of mathematical rigor and intuition." Peter Lakner, New York University

Feature

* Provides a rigorous treatment of financial theory in a casual style * Emphasizes computational examples * Introduces Financial engineering * Provides accessible introduction to financial models

Details ISBN1557869456 Language English ISBN-10 1557869456 ISBN-13 9781557869456 Media Book Format Hardcover Year 1997 Subtitle Discrete Time Models Short Title INTRO TO MATHEMATICAL F Edition 1st DOI 10.1604/9781557869456 UK Release Date 1997-04-15 AU Release Date 1997-04-15 NZ Release Date 1997-04-15 US Release Date 1997-04-15 Author Stanley R. Pliska Pages 272 Publisher John Wiley & Sons Inc Publication Date 1997-04-15 Imprint John Wiley & Sons Inc Place of Publication New York Country of Publication United States DEWEY 332.0151 Audience Undergraduate We've got this

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