Finance and Stochastics

, Volume 4, Issue 2, pp 117–146 | Cite as

Efficient hedging: Cost versus shortfall risk

  • Hans Föllmer
  • Peter Leukert

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.

Key words:Hedging, shortfall risk, efficient hedges, risk management, lower partial moments, convex duality, stochastic volatility 
JEL Classification:G10, G12, G13, D81 
Mathematics Subject Classification (1991):60H30, 62F03, 62P05, 90A09 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Hans Föllmer
    • 1
  • Peter Leukert
    • 1
  1. 1.Institut für Mathematik, Humboldt–Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany (e-mail: foellmer@mathematik.hu-berlin.de)DE

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