Der Itô-Kalkül: Einführung und Anwendungen / Edition 1

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More About This Textbook

Overview

Dieses Buch behandelt shastische Integrale bezüglich der Brownschen Bewegung (Itô-Integrale), den daraus resultierenden Itôschen Differentialkalkül und einige Anwendungen. Das Buch zeichnet sich durch zwei Besonderheiten aus: Zum Einen sind die mathematischen Voraussetzungen minimiert, und zum Anderen wird der Itô-Kalkül in einem ersten Schritt völlig ohne Martingale entwickelt. Dies erleichtert (insbesondere für Anwender) den Einstieg in die Theorie, da tiefer liegende shastische Methoden zunächst nicht benötigt werden. Erst in einem zweiten Schritt werden die engen Beziehungen zur Martingaltheorie und zur Browschen Bewegung entwickelt (Darstellungssätze, Sätze von Lévy, Girsanov, etc.). Anwendungen auf shastische Differentialgleichungen und Optionspreistheorie runden den Text ab.

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Product Details

  • ISBN-13: 9783540253921
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 9/21/2005
  • Language: German
  • Series: Springer-Lehrbuch Masterclass Series
  • Edition description: 2006
  • Edition number: 1
  • Pages: 256
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.54 (d)

Table of Contents

Mathematische Voraussetzungen.- Itô -Integrale für deterministische Integranden.- Anwendung: Lineare shastische Differentialgleichungen.- Itô-Integrale für shastische Integranden.- Der Itôsche Differentialkalkül.- Anwendung: Shastische Differentialgleichungen .- Martingale.- Darstellung Brownscher Martingale durch Itô-Integrale.- Itô-Integrale als zeittransformierte BBen.- Exponentielle Martingale.- Anwendung: Optionspreistheorie.- Lösung ausgewählter Aufgaben.- Häufige Bezeichnungen und Abkürzungen.- Literatur.- Sachverzeichnis.

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