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CAPITAL ALLOCATION AND RISK CONTRIBUTION WITH DISCRETE‐TIME COHERENT RISK

We define the capital allocation and the risk contribution for discrete‐time coherent risk measures and provide several equivalent representations of these objects. The formulations and the proofs are based on two instruments introduced in the paper: a probabilistic notion of the extreme system and a geometric notion of the generator. These notions are also of interest on their own and are important for other applications of coherent risk measures. All the concepts and results are illustrated by JP Morgan's Risk Metrics model.