Dual Divergence Estimators of the Tail Index

The main purpose of the present paper is to propose a new estimator of the tail index using -divergences and the duality technique. These estimators are explored with respect to robustness through the influence function approach. The empirical performances of the proposed estimators are illustrated by simulation.

Uniqueness for a Competing Species Model

We show that a martingale problem associated with a competing species model has a unique solution. The proof of uniqueness of the solution for the martingale problem is based on duality technique. It requires the construction of dual probability measures.

An Illustration of the Duality Technique in Semi-Continuous Linear Programming

We gıve a complete parametrıc solutıon of the followıng problem: Fınd a claım sıze dıstrıbutıon F on the fınıte ınterval [ο, ω], maxımizıng the stop-loss premıum correspondıng to a gıven excess e, under the constraınts that the fırst moment of F be at most equal to μ and the second at most equal to ν The method used ıs the dualıty technıque ın semı-contınuous lınear programmıng descrıbed in De Vylder (1978) Thıs technıque ıs summarızed, wıthout proofs, ın the fırst part of the paper.