Bruno de Finetti and the case of the critical line's last segment

The anticipatory views of Bruno de Finetti on portfolio theory, set out by the author in a 1940 article, have recently been discovered by Mark Rubinstein and reviewed by Harry Markowitz. This paper analyzes the crucial parts of de Finetti's paper and discusses the controversial issue of the critical line's last segment, i.e. the segment that leads to the minimum-variance efficient portfolio. Markowitz [Markowitz, Harry M., 2006. De Finetti scoops Markowitz. In: A Literature postscript. J. Invest. Manag. 4 (3), 3-18 (special issue)] derives the criterion for the last segment to lie on one of the boundaries of the set of legitimate portfolios in two (and n) dimensions and Pressacco [Pressacco, Flavio, 2005. De Finetti, Markowitz e la congettura dell'ultimo segmento. Rendiconti per gli Studi Economici Quantitativi, Universita  Ci  Foscari di Venezia] shows a necessary and sufficient condition for the last segment to lie inside the legitimate set in three dimensions when the correlations are uniformly positive. This paper revises the terms of the problem and completes the analysis.