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Efficient hedging: Cost versus shortfall risk

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  • Hans FÃllmer

    ()
    (Institut fØr Mathematik, Humboldt-UniversitÄt zu Berlin, Unter den Linden 6, 10099 Berlin, Germany Manuscript)

  • Peter Leukert

    ()
    (Institut fØr Mathematik, Humboldt-UniversitÄt zu Berlin, Unter den Linden 6, 10099 Berlin, Germany Manuscript)

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    Abstract

    An investor faced with a contingent claim may eliminate risk by (super-) hedging in a financial market. As this is often quite expensive, we study partial hedges which require less capital and reduce the risk. In a previous paper we determined quantile hedges which succeed with maximal probability, given a capital constraint. Here we look for strategies which minimize the shortfall risk defined as the expectation of the shortfall weighted by some loss function. The resulting efficient hedges allow the investor to interpolate in a systematic way between the extremes of no hedge and a perfect (super-) hedge, depending on the accepted level of shortfall risk.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 4 (2000)
    Issue (Month): 2 ()
    Pages: 117-146

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    Handle: RePEc:spr:finsto:v:4:y:2000:i:2:p:117-146

    Note: received: November 1998; final version received: March 1999
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    Web page: http://www.springerlink.com/content/101164/

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    Related research

    Keywords: Hedging; shortfall risk; efficient hedges; risk management; lower partial moments; convex duality; stochastic volatility;

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