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Mathematics of Financial Markets

  • Robert J. Elliott
  • P. Ekkehard Kopp

Part of the Springer Finance book series (FINANCE)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Robert J. Elliott, P. Ekkehard Kopp
    Pages 1-22
  3. Robert J. Elliott, P. Ekkehard Kopp
    Pages 23-43
  4. Robert J. Elliott, P. Ekkehard Kopp
    Pages 45-61
  5. Robert J. Elliott, P. Ekkehard Kopp
    Pages 63-74
  6. Robert J. Elliott, P. Ekkehard Kopp
    Pages 75-98
  7. Robert J. Elliott, P. Ekkehard Kopp
    Pages 99-133
  8. Robert J. Elliott, P. Ekkehard Kopp
    Pages 135-185
  9. Robert J. Elliott, P. Ekkehard Kopp
    Pages 187-210
  10. Robert J. Elliott, P. Ekkehard Kopp
    Pages 211-249
  11. Robert J. Elliott, P. Ekkehard Kopp
    Pages 251-270
  12. Back Matter
    Pages 271-292

About this book

Introduction

This work is aimed at an audience with asound mathematical background wishing to leam about the rapidly expanding field of mathematical finance. Its content is suitable particularly for graduate students in mathematics who have a background in measure theory and prob ability. The emphasis throughout is on developing the mathematical concepts re­ quired for the theory within the context of their application. No attempt is made to cover the bewildering variety of novel (or 'exotic') financial instru­ ments that now appear on the derivatives markets; the focus throughout remains on a rigorous development of the more basic options that lie at the heart of the remarkable range of current applications of martingale theory to financial markets. The first five chapters present the theory in a discrete-time framework. Stochastic calculus is not required, and this material should be accessible to anyone familiar with elementary probability theory and linear algebra. The basic idea of pricing by arbitrage (or, rather, by nonarbitrage) is presented in Chapter 1. The unique price for a European option in a single­ period binomial model is given and then extended to multi-period binomial models. Chapter 2 intro duces the idea of a martingale measure for price pro­ cesses. Following a discussion of the use of self-financing trading strategies to hedge against trading risk, it is shown how options can be priced using an equivalent measure for which the discounted price process is a mar­ tingale.

Keywords

arbitrage asset pricing Black-Scholes calculus derivatives linear algebra Martingal Martingale mathematics measure measure theory probability probability theory Rang stochastic calculus

Authors and affiliations

  • Robert J. Elliott
    • 1
  • P. Ekkehard Kopp
    • 2
  1. 1.Department of Mathematical SciencesUniversity of AlbertaEdmontonCanada
  2. 2.Pro-Vice-Chancellors’ OfficeThe University of HullHullUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-7146-6
  • Copyright Information Springer-Verlag New York 1999
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-7148-0
  • Online ISBN 978-1-4757-7146-6
  • Series Print ISSN 1616-0533
  • Series Online ISSN 2195-0687
  • Buy this book on publisher's site
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