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

Leonel Pérez-Hernández ()

No EC200505, Department of Economics and Finance Working Papers from Universidad de Guanajuato, Department of Economics and Finance

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. 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''.

Keywords: Partial Hedging; Efficient Hedging; Expected Loss; American Claims; Incomplete Markets; Dynamic Measures of Risk. (search for similar items in EconPapers)
JEL-codes: C61 C73 G19 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2005-10
New Economics Papers: this item is included in nep-fin and nep-rmg
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Published in Quantitative Finance (2007)

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