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| HAL : hal-00611323, version 1 |
| arXiv : 1106.4710 |
| Fiche détaillée |  Récupérer au format |
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| Physica A 390 (2011) 4340-4346 |
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| Proportionate vs disproportionate distribution of wealth of two individuals in a tempered Paretian ensemble |
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| G. Oshanin 1Yu. Holovatch 2 |
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| (2011) |
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| We study the distribution P(\omega) of the random variable \omega = x_1/(x_1 + x_2), where x_1 and x_2 are the wealths of two individuals selected at random from the same tempered Paretian ensemble characterized by the distribution \Psi(x) \sim \phi(x)/x^{1 + \alpha}, where \alpha > 0 is the Pareto index and $\phi(x)$ is the cut-off function. We consider two forms of \phi(x): a bounded function \phi(x) = 1 for L \leq x \leq H, and zero otherwise, and a smooth exponential function \phi(x) = \exp(-L/x - x/H). In both cases \Psi(x) has moments of arbitrary order. We show that, for \alpha > 1, P(\omega) always has a unimodal form and is peaked at \omega = 1/2, so that most probably x_1 \approx x_2. For 0 < \alpha < 1 we observe a more complicated behavior which depends on the value of \delta = L/H. In particular, for \delta < \delta_c - a certain threshold value - P(\omega) has a three-modal (for a bounded \phi(x)) and a bimodal M-shape (for an exponential \phi(x)) form which signifies that in such ensembles the wealths x_1 and x_2 are disproportionately different. |
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| 1 : | Laboratoire de Physique Théorique de la Matière Condensée (LPTMC) |
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CNRS : UMR7600 – Université Pierre et Marie Curie (UPMC) - Paris VI |
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| 2 : | Institute for Condensed Matter Physics |
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National Academy of Sciences of Ukraine |
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| 3 : | Laboratoire de Physique Théorique d'Orsay (LPT) |
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CNRS : UMR8627 – Université Paris XI - Paris Sud |
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| Domaine | : | Mathématiques/Probabilités Économie et finance quantitative/Finance Économie et finance quantitative/Econométrie de la finance Statistiques/Théorie |
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| Lien vers le texte intégral : |
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| http://fr.arXiv.org/abs/1106.4710 |
| hal-00611323, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00611323 | |
| oai:hal.archives-ouvertes.fr:hal-00611323 | |
| Contributeur : Patricia Dubois-Violette | |
| Soumis le : Mardi 26 Juillet 2011, 10:23:37 | |
| Dernière modification le : Mercredi 24 Avril 2013, 14:30:51 | |
