When Lorenz met Lyapunov

Marco Scarsini (1, 2) , Marco Dall'Aglio (3)

1 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC
2 Dipartimento di Scienze Economiche e Aziendali
3 Columbia University [New York]

We provide a simple characterization of the zonoid, lift zonoid, Lorenz zonoid of a random vector, as defined by Koshevoy and Mosler (J. Amer. Statist. Assoc. 91 (1996) 873; Bernoulli 4 (1998) 377). This characterization allows a direct use of Lyapunov's theorem on the range of nonatomic vector measures and therefore simplifies the proof of some results.

Keywords: Lorenz zonoid; lift zonoid; vector measure; Lyapunov's theorem.

Keywords: Lyapunov's theorem

Domains: Economy and decision science

Marco Scarsini, Marco Dall'Aglio. When Lorenz met Lyapunov. Statistics and Probability Letters, 2001, Vol. 54, N°1, pp. 101-105. ⟨10.1016/S0167-7152(01)00084-0⟩. ⟨hal-00540204⟩