Elementary Stochastic Calculus, with Finance in View / Edition 1

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Overview

Modelling with the Ito integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory.

This book is suitable for the reader without a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black-Scholes option pricing formula is derived. The book can serve as a text for a course on stochastic calculus for non-mathematicians or as elementary reading material for anyone who wants to learn about Ito calculus and/or stochastic finance.

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Product Details

  • ISBN-13: 9789810235437
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 10/28/1998
  • Series: Advanced Series on Statistical Science , #6
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 212
  • Sales rank: 1,012,114
  • Product dimensions: 5.80 (w) x 9.18 (h) x 0.37 (d)

Table of Contents

Reader Guidelines 1
1 Preliminaries 5
2 The Stochastic Integral 87
3 Stochastic Differential Equations 131
4 Applications of Stochastic Calculus in Finance 167
App. A1 Modes of Convergence 185
App. A2 Inequalities 187
App. A3 Non-Differentiability and Unbounded Variation of Brownian Sample Paths 188
App. A4 Proof of the Existence of the General Ito Stochastic Integral 190
App. A5 The Radon-Nikodym Theorem 193
App. A6 Proof of the Existence and Uniqueness of the Conditional Expectation 194
Bibliography 195
Index 199
List of Abbreviations and Symbols 209
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