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

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  • Leonel Perez-hernandez

Abstract

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.

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  • 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

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    Cited by:

    1. Peter Lindberg, 2012. "Optimal partial hedging of an American option: shifting the focus to the expiration date," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(3), pages 221-243, June.
    2. Erdnç Akyildirim & Albert Altarovici, 2016. "Partial hedging and cash requirements in discrete time," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 929-945, June.
    3. Sabrina Mulinacci, 2011. "The efficient hedging problem for American options," Finance and Stochastics, Springer, vol. 15(2), pages 365-397, June.
    4. Mustafa Ç. Pinar, 2010. "Buyer's quantile hedge portfolios in discrete-time trading," Quantitative Finance, Taylor & Francis Journals, vol. 13(5), pages 729-738, October.

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