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Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory

Elena Di Bernardino, Thomas Laloë, Véronique Maume-Deschamps, Clémentine Prieur (2013)

ESAIM: Probability and Statistics

This paper deals with the problem of estimating the level sets L(c) =  {F(x) ≥ c}, with c ∈ (0,1), of an unknown distribution function F on ℝ+2. A plug-in approach is followed. That is, given a consistent estimator Fn of F, we estimate L(c) by Ln(c) =  {Fn(x) ≥ c}. In our setting, non-compactness property is a priori required for the level sets to estimate. We state consistency results with respect to the Hausdorff distance and the volume of the symmetric difference. Our results are motivated by...

Pôles, intermédiaires et centres dans un groupe d'opinions

J. Feldman (1973)

Mathématiques et Sciences Humaines

Les opinions dont il s'agit sont des ordres totaux sur un ensemble d'objets. Par rapport à un groupe d'opinions exprimées, on définit les notions d'opinions «pôles», «intermédiaires» et «centres» : ces derniers peuvent servir de choix collectifs et on examine quelques-unes de leurs propriétés ; en particulier, ils appartiennent à l'intervalle convexe engendré par les opinions exprimées, autrement dit, ils conservent les avis unanimes.

Portfolio optimization for pension plans under hybrid stochastic and local volatility

Sung-Jin Yang, Jeong-Hoon Kim, Min-Ku Lee (2015)

Applications of Mathematics

Based upon an observation that it is too restrictive to assume a definite correlation of the underlying asset price and its volatility, we use a hybrid model of the constant elasticity of variance and stochastic volatility to study a portfolio optimization problem for pension plans. By using asymptotic analysis, we derive a correction to the optimal strategy for the constant elasticity of variance model and subsequently the fine structure of the corrected optimal strategy is revealed. The result...

Poset-valued preference relations

Vladimír Janiš, Susana Montes, Branimir Šešelja, Andreja Tepavčević (2015)

Kybernetika

In decision processes some objects may not be comparable with respect to a preference relation, especially if several criteria are considered. To provide a model for such cases a poset valued preference relation is introduced as a fuzzy relation on a set of alternatives with membership values in a partially ordered set. We analyze its properties and prove the representation theorem in terms of particular order reversing involution on the co-domain poset. We prove that for every set of alternatives...

Poverty measures and poverty orderings.

Miguel A. Sordo, Héctor M. Ramos, Carmen D. Ramosm (2007)

SORT

We examine the conditions under which unanimous poverty rankings of income distributions can be obtained for a general class of poverty indices. The "per-capita income gap" and the Shorrocks and Thon poverty measures are particular members of this class. The conditions of dominance are stated in terms of comparisons of the corresponding TIP curves and areas.

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