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On the existence of an efficient hedge for an American contingent claim within a discrete time market


  • Leonel Perez-hernandez


We show the existence of efficient hedge strategies for an investor facing the problem of a lack of initial capital for implementing a (super-) hedging strategy for an American contingent claim in a general incomplete market. In order to optimize we consider the maximization of the expected success ratio of the worst possible case as well as the minimization of the shortfall risk. These problems lead to stochastic games which do not need to have a value. We provide an example for this in a CRR model for an American put option. Alternatively we might fix a minimal expected success ratio or a boundary for the shortfall risk and look for the minimal amount of initial capital for which there is a self-financing strategy fulfilling one or the other restriction. For all these problems we show the optimal strategy consists in hedging a modified American claim [image omitted] for some 'randomized test process' ϕ.

Suggested Citation

  • Leonel Perez-hernandez, 2007. "On the existence of an efficient hedge for an American contingent claim within a discrete time market," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 547-551.
  • Handle: RePEc:taf:quantf:v:7:y:2007:i:5:p:547-551 DOI: 10.1080/14697680601158700

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    References listed on IDEAS

    1. Schweizer, Martin, 1991. "Option hedging for semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 339-363, April.
    2. Föllmer, Hans & Wu, Ching-Tang & Yor, Marc, 1999. "Canonical decomposition of linear transformations of two independent Brownian motions motivated by models of insider trading," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 137-164, November.
    3. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 385-413.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    5. Rüdiger Frey, 2000. "Risk Minimization with Incomplete Information in a Model for High-Frequency Data," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 215-225.
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    Cited by:

    1. Sabrina Mulinacci, 2011. "The efficient hedging problem for American options," Finance and Stochastics, Springer, vol. 15(2), pages 365-397, June.


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