F Broeckx

Ordering of Risks and Ruin Probabilities

Abstract Upper and lower bounds for the ruin probability over infinite time in the classical actuarial risk model are derived (usual independence and equidistribution assumptions, the claim number process being Poisson). Some recent results on bounds for certain classes of integrals are adapted to the case of a convolution transform in order to derive applicable (from the actuarial point of view) bounds.

Decomposing stochastic frontier efficiency into secular and organisational efficiency

Abstract In this article we propose to decompose the frontier efficiency into two distinct parts, namely a secular part (long-term) and an organisational part (short-term). A product life-cycle model for twelve industries of the Belgian manufacturing sector has been tested for the period 1979–1983 by using cluster analysis. Filtering out the secular effect for each cluster (groups of fimrs) makes it possible to decompose the overall technical efficiency. It turns out that for 27 out of 44 groups of firms the organisational part is larger than the secular part. Considering the status of the firms, organisational efficiency differences could be analysed directy for groups of similar firms.

Economic performance and “frontier” efficiency: A product life-cycle approach

We propose to introduce some economic performance variables of the firms and relate these with the corresponding “frontier” efficiency measures of 13 industries of the Belgian manufacturing sector in 1978. In order to find groups of similar firms by applying a cluster technique, we assume that this relationship is of a product life cycle nature.In the light of the product life cycle scheme itself and variations of it we can consider the possible explanatory variables of technical inefficiency in each group of firms as sources which intensify or slow-down the economic performance of the firm under consideration. Some cautious characterization of the top and bottom level clusters is formulated and linked to the efficiency issue.

Numerical evaluation of bounded bayesian parameters in case of autocorrelated errors and multicollinearity in data

ZusammenfassungIm Rahmen der Bayes’schen Theorie wird eine neue Methode zur Parameterermittlung entwickelt, für die als a-priori-Information Gleichverteilung in einem Intervall gegeben ist. Diese Methode ist geeignet, um autokorrelierte Fehler sowie Multikollinearität der Daten zu eliminieren.Im Speziellen wird der Fall zweier beschränkter Parameter zur Schätzung der Cobb-Douglas-Funktion betrachtet. Die Ergebnisse werden in einem nichttrivialen Beispiel kommentiert; sie werden verglichen mit ähnlichen Lösungen nach der Methode der kleinsten Quadrate, die im Fall schwerer Multikollinearität nicht geeignet ist.Der Artikel verwendet die abkürzende Matrizenterminologie; er vermeidet lange algebraische Rechnungen, die jedoch von den Autoren nachgeliefert werden können.SummaryA new method is given for evaluation, in a Bayesian framework, of parameters, from which is known as prior-information that they are uniformly distributed in an interval. The method is appropriated to eliminate autocorrelated errors, and multicollinearity in the data.The case of two bounded parameters is especially considered in estimating the Cobb-Douglas production functions.Results are commented in a non trivial example, and compared with the simular least square solution, which is not appropriated as estimation method in case of severe multicollinearity. The paper is presented in a short matrix-notation, avoiding long algebraic calculations, which can be delivred by the authors.RésuméUne nouvelle méthode d’évaluation de paramètres est donnée dans le cadre de la théorie bayesienne, dont on sait, par une information antérieure, qu’ils sont distribués uniformément dans un intervalle. La méthode est appropriée pour éliminer les autocorrélations d’erreurs, et la multicollinéarité dans les données.Le cas de deux paramètres limités fait l’objet d’une considération particulière dans l’estimation d’une fonction de production Cobb-Douglas. Les résultats sont préscrits dans un exemple significatif, et comparés avec la solution sembable par la mðhode de moindres carrées, qui n’est pas une méthode d’estimation appropriée dans le cas d’une multicollinéarité forte.Dans l’article le calcul matricielle abrévié est utilisé, eliminant des longs calculs algébraiques, qui peuvent être transmis par les auteurs.РезюмеВ рамках теории Баеса развивается новый метод для определения параметров, в котором равное распределение в одном интервале является априорной информацией. Этот метод пригодный для исключения самокоррелированных ощибок и мультиколлинеарнос ти данных. Подробно рассматривается случай двух ограниченных параметров для оценки функции Кобб-Лугляса. Результаты толкуются на нетривиальном примере; они сравняются с подобными рещениями по методу малейщих квадратов, который непригодный для случая сильной мультиколлинеарнос ти.В Этой статье применяется короткая матричная терминология; избегаются долгие алгебраические исчисления, которые однако авторы могут доставить дополнительно.