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The Black–Litterman model extends the framework of the Markowitz modern portfolio theory to incorporate investor views. The authors consider a case in which multiple view estimates, including uncertainties, are given for the same underlying subset of assets at a point in time. This motivates their consideration of data fusion techniques for combining information from multiple sources. In particular, they consider consistency-based methods that yield fused view and uncertainty pairs; such methods are not common to the quantitative finance literature. They show a relevant, modern case of incorporating machine learning model-derived view and uncertainty estimates, and the impact on portfolio allocation, with an example subsuming arbitrage pricing theory. Hence, they show the value of the Black– Litterman model in combination with information fusion and artificial intelligence–grounded prediction methods.

Original publication




Journal article


Journal of Financial Data Science

Publication Date





23 - 49