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Efficient hedging: Cost versus shortfall risk

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Author Info
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)
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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Publisher 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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Related research
Keywords: Hedging; shortfall risk; efficient hedges; risk management; lower partial moments; convex duality; stochastic volatility;

Other versions of this item:

Find related papers by JEL classification:
G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

Cited by:
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  1. H. Föllmer & A. Schied, . "Convex measures of risk and trading constraints," Sonderforschungsbereich 373 2001-71, Humboldt Universitaet Berlin.
    Other versions:
  2. Heinz Weisshaupt, 2003. "Insuring against the shortfall risk associated with real options," Decisions in Economics and Finance, Springer, vol. 26(2), pages 81-96, November. [Downloadable!] (restricted)
  3. Michael Kohlmann & Shanjian Tang, 2000. "Recent Advances in Backward Stochastics Ricatti Equations and Their Applications," CoFE Discussion Paper 00-30, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
  4. Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January. [Downloadable!] (restricted)
    Other versions:
  5. Michael Kohlmann & Shanjian Tang, 2000. "Multi-Dimensional Backward Stochastic Ricatti Equations, and Applications," CoFE Discussion Paper 00-29, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
  6. Matos, Joao Amaro de & Lacerda, Ana, 2006. "Equilibrium Bid-Ask Spread of European Derivatives in Dry Markets," FEUNL Working Paper Series wp480, Universidade Nova de Lisboa, Faculdade de Economia. [Downloadable!]
  7. Leonel Pérez-Hernández, . "On the Existence of Efficient Hedge for an American Contingent Claim: Discrete Time Market," School of Economics Working Papers EC200505, Universidad de Guanajuato. [Downloadable!]
  8. Michael Kohlmann & Shanjian Tang, 2000. "Global Adapted Solution of One-Dimensional Backward Stochastic Riccati Equations, with Application to the Mean-Variance Hedging," CoFE Discussion Paper 00-26, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
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