Skip to main content

The Notion of Arbitrage and Free Lunch in Mathematical Finance

  • Chapter
Aspects of Mathematical Finance

We shall explain the concepts alluded to in the title in economic as well as in mathematical terms. These notions play a fundamental role in the modern theory of mathematical finance. We start by presenting the ideas in a very informal style and then gradually raise the level of mathematical formalisation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 49.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 49.99
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

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. Bachelier (1900), Théorie de la Speculation. Ann. Sci. Ecole Norm. Sup., Vol. 17, pp. 21–86, [English translation in: The Random Character of stock prices (P. Cotner, editor), MIT, Cambridge, MA, 1964]

    MathSciNet  Google Scholar 

  2. F. Black, M. Scholes (1973), The pricing of options and corporate liabilities. J. Polit. Econ., Vol. 81, pp. 637–659

    Article  Google Scholar 

  3. F. Delbaen, W. Schachermayer (1994), A general version of the fundamental theorem of asset pricing. Math. Annalen, Vol. 300, pp. 463–520

    Article  MATH  MathSciNet  Google Scholar 

  4. F. Delbaen, W. Schachermayer (1998), The fundamental theorem of asset pricing for unbounded stochastic processes. Math. Annalen, Vol. 312, pp. 215–250

    Article  MATH  MathSciNet  Google Scholar 

  5. F. Delbaen, W. Schachermayer (2004), What is a Free Lunch? Not. AMS, Vol. 51, No. 5, pp. 526–528

    MATH  MathSciNet  Google Scholar 

  6. J.M. Harrison, S.R. Pliska (1981), Martingales and stochastic integrals in the theory of continuous trading. Stoch. Proc. Appl., Vol. 11, pp. 215–260

    Article  MATH  MathSciNet  Google Scholar 

  7. D.M. Kreps (1981), Arbitrage and equilibrium in economies with infinitely many commodities. J. Math. Econ., Vol. 8, pp. 15–35

    Article  MATH  MathSciNet  Google Scholar 

  8. D. Revuz, M. Yor (1991), Continuous Martingales and Brownian Motion. Springer, Berlin Heidelberg New York

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Schachermayer, W. (2008). The Notion of Arbitrage and Free Lunch in Mathematical Finance. In: Yor, M. (eds) Aspects of Mathematical Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75265-3_3

Download citation

Publish with us

Policies and ethics