Efficient hedging: Cost versus shortfall risk - Hans Föllmer; Peter Leukert (Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, 1999)
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.
urn:nbn:de:kobv:11-10056108
Keywords: G10; G12; G13; D81; 330; risk management; stochastic volatility; shortfall risk; Hedging; efficient hedges; lower partial moments; convex duality