Skip to main content
Log in

Asymptotic pricing in large financial markets

  • Original Article
  • Published:
Mathematical Methods of Operations Research Aims and scope Submit manuscript

Abstract

The problem of hedging and pricing sequences of contingent claims in large financial markets is studied. Connection between asymptotic arbitrage and behavior of the α-quantile price is shown. The large Black–Scholes model is carefully examined.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Delbaen F, Schachermayer W (1998)The fundamental theorem of asset pricing for unbounded stochastic processes. Math Ann 312:215–250

    Article  MATH  MathSciNet  Google Scholar 

  • Föllmer H, Kabanov YuM (1998) Optional decomposition and Lagrange multipliers. Finance Stoch 2:69–81

    MATH  MathSciNet  Google Scholar 

  • Föllmer H, Kramkov DO (1997) Optional decompositions under constraints. Probab Theory Relat Fields 109:1–25

    Article  MATH  Google Scholar 

  • Föllmer H, Leukert P (1999) Quantile hedging. Finance Stoch 3:251–273

    Article  MATH  MathSciNet  Google Scholar 

  • Jacod J, Shiryaev AN (1987) Limit theorems for stochastic processes. Springer, Berlin Heidelberg New York

    MATH  Google Scholar 

  • Jacod J, Shiryaev AN (1998) Local martingales and the fundamental asset pricing theorems in the discrete-time case. Finance Stoch 2:259–273

    Article  MATH  MathSciNet  Google Scholar 

  • Kabanov YuM, Kramkov DO (1994) Large financial markets: asymptotic arbitrage and contiguity. Probab Theory Appl 39(1):182–187

    Article  MathSciNet  Google Scholar 

  • Kabanov YuM, Kramkov DO (1998) Asymptotic arbitrage in large financial markets. Finance Stoch 2(2):143–172

    Article  MATH  MathSciNet  Google Scholar 

  • Klein I (2000) A fundamental theorem of asset pricing for large financial markets. Math Finance 10(4):443–458

    Article  MATH  MathSciNet  Google Scholar 

  • Klein I, Schachermayer W (1996) Asymptotic arbitrage in non-complete large financial markets. Probab Theory Appl 41(4):780–788

    MATH  MathSciNet  Google Scholar 

  • Kramkov DO (1996) Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets. Probab Theory Relat Fields 105:459–479

    Article  MATH  MathSciNet  Google Scholar 

  • Rásonyi M (2002) On certain problems of arbitrage theory in discrete time financial market models. PhD thesis

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michał Baran.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baran, M. Asymptotic pricing in large financial markets. Math Meth Oper Res 66, 1–20 (2007). https://doi.org/10.1007/s00186-006-0144-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00186-006-0144-7

Keywords

Mathematics Subject Classification (2000)

JEL Classification

Navigation