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In this paper, we seek to find the optimal retentions for an insurance company which intends to reinsure each of n risks belonging to its portfolio, by means of a pure quota-share treaty, a pure excess of loss treaty or any combination of the two. The criterion chosen to the selection of the optimal programme is the maximization of the adjustment coefficient, attending to the relationship existing between this coefficient and Lundberg's upper bound of the ruin probability.

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The health benefits of physical activity have been demonstrated. However, there is a growing debate over the potential adverse effects of strenuous physical activity, particularly at a professional level. The goal of this work is to investigate whether elite athletes live longer than general populations, by a comprehensive survival analysis of two populations of professional football players. Lifespan data of Portuguese and Spanish football players, who have repre-sented the national teams, were collected. The mortality of each cohort is then compared to that of the respective standard population, using data available in the Human Mortality Database and four different approaches. At the end, a comparison between the mortality of Portuguese and Spanish football players is also carried out. Keywords: elite football players, mortality measures, Portugal, Spain. Resumen Los beneficios para la salud derivados del ejercicio regular están científicamente probados. Sin embargo, cuando se trata de deportistas profesionales, cuya actividad física es muy intensa, los beneficios ya no son una evidencia clara. El objetivo de este trabajo es investigar si los deportistas de élite viven más tiempo que la población general. Se recogieron datos sobre la fecha de nacimiento y muerte (en su caso) de los jugadores portugueses y españoles que representaron su selección, así como otras variables de interés. Cada grupo de jugadores se compara con la población general del país respectivo, utilizando los datos disponibles en la Human Mortality Database y cuatro enfoques diferentes. Al final, también se compara la mortalidad de futbolistas portugueses y españoles. Palabras clave: futbolistas de élite, medidas de mortalidad, España, Portugal.