Journal of Risk

Fully flexible extreme views

Attilio Meucci, David Ardia, Simon Keel


We extend the entropy pooling generalization of the Black-Litterman approach to effectively handle extreme views on the tails of a distribution. First, we provide a recursive algorithm to process views on conditional value-at-risk, which cannot be handled directly by the original implementation of entropy pooling. Second, we represent both the prior and the posterior distribution on a grid, instead of using Monte Carlo scenarios. This way it becomes possible to parsimoniously cover even the far tails of the underlying distribution. Documented code is available to download (see

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