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  • © 2006

The Mathematics of Arbitrage

  • The fundamental theorem of Asset Pricing due to Delbaen and Schachermayer was a milestone in the history of modern mathematical finance and now forms the cornerstone of this book
  • Puts into book format a series of major results due mostly to the 2 authors of this book
  • Embeds highest-level research results into a treatment amenable to graduate students, with introductory, explanatory background
  • Long-awaited in the quantitative finance community
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Finance (FINANCE)

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Table of contents (15 chapters)

  1. Front Matter

    Pages I-XVI
  2. A Guided Tour to Arbitrage Theory

    1. Front Matter

      Pages 1-1
    2. The Story in a Nutshell

      • Freddy Delbaen, Walter Schachermayer
      Pages 3-9
    3. Models of Financial Markets on Finite Probability Spaces

      • Freddy Delbaen, Walter Schachermayer
      Pages 11-32
    4. Utility Maximisation on Finite Probability Spaces

      • Freddy Delbaen, Walter Schachermayer
      Pages 33-56
    5. Bachelier and Black-Scholes

      • Freddy Delbaen, Walter Schachermayer
      Pages 57-69
    6. The Kreps-Yan Theorem

      • Freddy Delbaen, Walter Schachermayer
      Pages 71-83
    7. The Dalang-Morton-Willinger Theorem

      • Freddy Delbaen, Walter Schachermayer
      Pages 85-109
    8. A Primer in Stochastic Integration

      • Freddy Delbaen, Walter Schachermayer
      Pages 111-128
    9. Arbitrage Theory in Continuous Time: an Overview

      • Freddy Delbaen, Walter Schachermayer
      Pages 129-146
  3. The Original Papers

    1. Front Matter

      Pages 147-147
    2. A General Version of the Fundamental Theorem of Asset Pricing (1994)

      • Freddy Delbaen, Walter Schachermayer
      Pages 149-205
    3. The No-Arbitrage Property under a Change of Numéraire (1995)

      • Freddy Delbaen, Walter Schachermayer
      Pages 217-230
    4. The Existence of Absolutely Continuous Local Martingale Measures (1995)

      • Freddy Delbaen, Walter Schachermayer
      Pages 231-250
    5. The Banach Space of Workable Contingent Claims in Arbitrage Theory (1997)

      • Freddy Delbaen, Walter Schachermayer
      Pages 251-278
  4. Back Matter

    Pages 357-373

Reviews

From the reviews:

"As a learning device, I think this works really well. The second half of the book allows readers to ‘put to use’ the mathematics they learn in the first half. I really like the authors’ writing style. They provide plenty of intuitive insights and historical notes along the way as they formally develop concepts. … I recommend it highly to theoretically-inclined financial engineers and researchers." (www.riskbook.com, September, 2006)

"The aim of the book, as the authors state … is to give the reader a guided tour through the mathematics of arbitrage. … The book will be of invaluable help to new researchers in the area of incomplete markets. A new graduate student wishing to do such research would start by reading the papers in the book. She or he now has a very good book to assist this study." (Angelos Dassios, Mathematical Reviews, Issue 2007 a)

About the authors

Walter Schachermeyer, born in 1950 in Linz, Austria, has received--as the first mathematician--the 1998 Wittgenstein Award, Austria's highest honor for scienctific achievement. Since 1998 he holds the Chair for Actuarial and Financial Mathematics at the Vienna University of Technolgoy. Among his achievements is the proof of the "Fundamental Theorem of Asset Pricing" in its general form, which was done in joint work with Freddy Delbaen.

Freddy Delbaen, born in 1946 in Duffel/Antwerpen, Belgium, is Professor for Financial Mathematics at the ETH in Zurich since 1995.

Bibliographic Information

Buy it now

Buying options

eBook USD 109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access