Abstract

The idea of efficient hedging has been introduced by Föllmer and Leukert. They defined the shortfall risk as the expectation of the shortfall weighted by a loss function, and looked for strategies that minimize the shortfall risk under a capital constraint. In this paper, to measure the shortfall risk, we use the coherent risk measures introduced by Artzner, Delbaen, Eber and Heath. We show that, for a given contingent claim H, the optimal strategy consists in hedging a modified claim ϕH for some randomized test ϕ. This is an analogue of the results by Föllmer and Leukert.

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