Efficient hedging: Cost versus shortfall risk

Hans FÃllmer () and Peter Leukert ()
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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

Finance and Stochastics, 2000, vol. 4, issue 2, 117-146

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.

Keywords: Hedging; shortfall risk; efficient hedges; risk management; lower partial moments; convex duality; stochastic volatility (search for similar items in EconPapers)
JEL-codes: D81 G10 G12 G13 (search for similar items in EconPapers)
Date: 2000-02-10
Note: received: November 1998; final version received: March 1999
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Citations: View citations in EconPapers (83)

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