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Cover: 9781441928627 | Stochastic Calculus and Financial Applications | J. Michael Steele | X
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Stochastic Calculus and Financial Applications
Taschenbuch von J. Michael Steele
Sprache: Englisch

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Beschreibung
This book is designed for students who want to develop professional skill in stochastic calculus and its application to problems in finance. The Wharton School course that forms the basis for this book is designed for energetic students who have had some experience with probability and statistics but have not had ad­ vanced courses in stochastic processes. Although the course assumes only a modest background, it moves quickly, and in the end, students can expect to have tools that are deep enough and rich enough to be relied on throughout their professional careers. The course begins with simple random walk and the analysis of gambling games. This material is used to motivate the theory of martingales, and, after reaching a decent level of confidence with discrete processes, the course takes up the more de­ manding development of continuous-time stochastic processes, especially Brownian motion. The construction of Brownian motion is given in detail, and enough mate­ rial on the subtle nature of Brownian paths is developed for the student to evolve a good sense of when intuition can be trusted and when it cannot. The course then takes up the Ito integral in earnest. The development of stochastic integration aims to be careful and complete without being pedantic.
This book is designed for students who want to develop professional skill in stochastic calculus and its application to problems in finance. The Wharton School course that forms the basis for this book is designed for energetic students who have had some experience with probability and statistics but have not had ad­ vanced courses in stochastic processes. Although the course assumes only a modest background, it moves quickly, and in the end, students can expect to have tools that are deep enough and rich enough to be relied on throughout their professional careers. The course begins with simple random walk and the analysis of gambling games. This material is used to motivate the theory of martingales, and, after reaching a decent level of confidence with discrete processes, the course takes up the more de­ manding development of continuous-time stochastic processes, especially Brownian motion. The construction of Brownian motion is given in detail, and enough mate­ rial on the subtle nature of Brownian paths is developed for the student to evolve a good sense of when intuition can be trusted and when it cannot. The course then takes up the Ito integral in earnest. The development of stochastic integration aims to be careful and complete without being pedantic.
Zusammenfassung
Stochastic calculus has important applications to mathematical finance. This book will appeal to practitioners and graduate students who want an elementary introduction to these areas.
Inhaltsverzeichnis
Random Walk and First Step Analysis * First Martingale Steps * Brownian Motion * Martingale--Next Steps * Richness of Paths * Itô Integration * Localization and Itô's Integral * Itô's Formula * Stochastic Differential Equations * Arbitrage and SDE's * The Diffusion Equation * Representation Theorems * Girsanov Theory * Arbitrage and Martingales * The Feynman-Kac Connection
Details
Erscheinungsjahr: 2010
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 312
Reihe: Stochastic Modelling and Applied Probability
Inhalt: x
302 S.
3 s/w Illustr.
ISBN-13: 9781441928627
ISBN-10: 1441928626
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Steele, J. Michael
Auflage: Softcover reprint of the original 1st ed. 2001
Hersteller: Springer US
Springer New York
Stochastic Modelling and Applied Probability
Maße: 235 x 155 x 17 mm
Von/Mit: J. Michael Steele
Erscheinungsdatum: 01.12.2010
Gewicht: 0,476 kg
preigu-id: 107174320
Zusammenfassung
Stochastic calculus has important applications to mathematical finance. This book will appeal to practitioners and graduate students who want an elementary introduction to these areas.
Inhaltsverzeichnis
Random Walk and First Step Analysis * First Martingale Steps * Brownian Motion * Martingale--Next Steps * Richness of Paths * Itô Integration * Localization and Itô's Integral * Itô's Formula * Stochastic Differential Equations * Arbitrage and SDE's * The Diffusion Equation * Representation Theorems * Girsanov Theory * Arbitrage and Martingales * The Feynman-Kac Connection
Details
Erscheinungsjahr: 2010
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 312
Reihe: Stochastic Modelling and Applied Probability
Inhalt: x
302 S.
3 s/w Illustr.
ISBN-13: 9781441928627
ISBN-10: 1441928626
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Steele, J. Michael
Auflage: Softcover reprint of the original 1st ed. 2001
Hersteller: Springer US
Springer New York
Stochastic Modelling and Applied Probability
Maße: 235 x 155 x 17 mm
Von/Mit: J. Michael Steele
Erscheinungsdatum: 01.12.2010
Gewicht: 0,476 kg
preigu-id: 107174320
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