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On the Existence of Efficient Hedge for an American Contingent Claim: Discrete Time Market

  • Leonel Pérez-Hernández


    (Department of Economics and Finance, Universidad de Guanajuato)

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    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. For the optimization we consider once 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. 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 for some ``randomized test process''.

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    Paper provided by Universidad de Guanajuato, Department of Economics and Finance in its series Department of Economics and Finance Working Papers with number EC200505.

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    Length: 22 pages
    Date of creation: Oct 2005
    Date of revision:
    Publication status: Published in Quantitative Finance (2007)
    Handle: RePEc:gua:wpaper:ec200505
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