Efficient hedging with coherent risk measure
According to the definition of Föllmer and Leukert, the shortfall risk is the expectation of the shortfall weighted by a loss function, and looked for strategies that minimize the shortfall risk under a capital constraint. In order to measure the shortfall risk, the author uses coherent risk measures proposed by Artzener, Delbaen, Eber and Heath. On the basis of a representation result in the case of coherent \(L^1\)-lower-semicontinuous risk measures, it is proved that, for a given contingent claim \(H\), the optimal strategy consists in hedging a modified claim \(\phi H\), for some randomized test \(\phi\) (i.e. \(\phi:\Omega\to[0,1]\), with \(\phi\) measurable, given the probability space \((\Omega, F,P)\)). Finally some cases involving special coherent risk measures are considered, as the worst conditional expectation.
scientific article; zbMATH DE number 2082148