Geometric properties of multivariate correlation in de Finetti’s approach to insurance theory

We provide proofs and commentary on parts of Bruno De Finetti’s paper ”About Correlation”. In particular we focus on De Finetti’s angle theorem, which he stated without proof and whose striking simplicity and power would seem to make it a natural candidate for any multivariate statistics text. We establish a connection between de Finetti’s angle theorem and ongoing research on the boundary of the convex set of correlation matrices. We also provide evidence from this article that de Finetti discovered rank correlation before or at the same time as Kendall. 1. Università di Roma 1,00183, Rome, Italy and Courant Institute; 2. Baruch College, 1 Bernard Baruch way, New York, NY 10010; 3.Goldman Sachs, London UK