Solvabilité II

Selon l’Autorité Européenne des Assurances et des Pensions Professionnelles (AEAPP) (European Insurance and Occupational Pensions Authority (EIOPA), en anglais), “Solvabilité II est un projet qu’a comme objectif réviser le régime de surveillance des entreprises d’assurance et réassurance dans l’Union Européenne. Le premier pas a été l’adoption en Novembre de 2009 de la Directive Solvabilité II.” Ce document présente les concepts clés et les principales formules de calcul quantitatif inclus dans Solvabilité II. Ce document est le résultat de la préparation et l’enseignement du point 4 du cours «Solvabilité» du Master en Sciences Actuarielles et Financières de l’Université de Barcelone. Cette version en français est le résultat de la participation dans la “Formation des formateurs” en collaboration avec l’ISFA de l’Université de Lyon-I

Equilibrium distributions and discrete Schur-constant models

This paper introduces Schur-constant equilibrium distribution models of dimension n for arithmetic non-negative random variables. Such a model is defined through the (several orders) equilibrium distributions of a univariate survival function. First, the bivariate case is considered and analyzed in depth, stressing the main characteristics of the Poisson case. The analysis is then extended to the multivariate case. Several properties are derived, including the implicit correlation and the distribution of the sum

Some optimization and decision problems in proportional reinsurance [WP]

Reinsurance is one of the tools that an insurer can use to mitigate the underwriting risk and then to control its solvency. In this paper, we focus on the proportional reinsurance arrangements and we examine several optimization and decision problems of the insurer with respect to the reinsurance strategy. To this end, we use as decision tools not only the probability of ruin but also the random variable deficit at ruin if ruin occurs. The discounted penalty function (Gerber & Shiu, 1998) is employed to calculate as particular cases the probability of ruin and the moments and the distribution function of the deficit at ruin if ruin occurs

Some optimization and decision problems in proportional reinsurance

Reinsurance is one of the tools that an insurer can use to mitigate the underwriting risk and then to control its solvency. In this paper, we focus on the proportional reinsurance arrangements and we examine several optimization and decision problems of the insurer with respect to the reinsurance strategy. To this end, we use as decision tools not only the probability of ruin but also the random variable deficit at ruin if ruin occurs. The discounted penalty function is employed to calculate as particular cases the probability of ruin and the moments and the distribution function of the deficit at ruin if ruin occurs. We consider the classical risk theory model assuming a Poisson process and an individual claim amount phase-type distributed, modified with a proportional reinsurance with a retention level that is not constant and depends on the level of the surplus. Depending on whether the initial surplus is below or above a threshold level, the discounted penalty function behaves differently. General expressions for this discounted penalty function are obtained, as well as interesting theoretical results and explicit expressions for phase-type 2 distribution. These results are applied in numerical examples of decision problems based on the probability of ruin and on different risk measures of the deficit at ruin if ruin occurs (the expectation, the Value at Risk and the Tail Value at Risk)

Deficit at ruin with threshold proportional reinsurance

In this paper, we focus our analysis on the distribution function and the moments of the deficit at ruin in a model with a threshold proportional reinsurance strategy using the Gerber-Shiu function. This strategy considers a proportional reinsurance, but the retention level is not constant and depends on the surplus. Then a retention level k1 is applied whenever the surplus is less than a specific threshold b, and a retention level k2 is applied in the other case. In a Poisson risk model, we derive the integro-differential equation for the Gerber-Shiu function when the claim amount is exponentially distributed. Then, we obtain the analytical expression for the Gerber-Shiu function for a set of penalty functions. This analytical expression is applicable for several penalty functions and includes, among others, the ruin probability, the time of ruin and the distribution function of the deficit at ruin

Mètodes mixtos en la investigació de les ciències de l’activitat física i l’esport

La investigació en les ciències de l’activitat física i l’esport ha estat influenciada prioritàriament per procediments quantitatius adaptats d’altres àrees del coneixement. L’aparició de nous paradigmes, mètodes i procediments d’investigació ens ofereix un nombre més gran de possibilitats de combinació d’instruments per a l’anàlisi de l’activitat física i l’esport que pot enriquir tot el procés investigador. En aquest article presentem, mitjançant exemples d’investigacions, els mètodes mixtos (Mixed Method Approach), que proposen conjugar dades de naturalesa quantitativa i qualitativa en el mateix estudi. Aquesta nova perspectiva metodològica s’està refermant amb força en l’última dècada d’acord amb la necessitat actual de plantejaments més integrats en la investigació de la motricitat humana

Métodos mixtos en la investigación de las ciencias de la actividad física y el deporte

La investigación en las ciencias de la actividad física y el deporte ha estado influenciada prioritariamente por procedimientos cuantitativos adaptados de otras áreas del conocimiento. La aparición de nuevos paradigmas, métodos y procedimientos de investigación nos ofrecen mayor número de posibilidades de combinación de instrumentos para el análisis de la actividad física y el deporte que puede enriquecer todo el proceso investigador. En este artículo presentamos, mediante ejemplos de investigaciones, los métodos mixtos (Mixed Method Approach) que proponen conjugar datos de naturaleza cuantitativa y cualitativa en el mismo estudio. Esta nueva perspectiva metodológica se está afianzando con fuerza en la última década acorde con la necesidad actual de planteamientos más integrados en la investigación de la motricidad humana

Discrete Schur-constant models

This paper introduces a class of Schur-constant survival models, of dimension n, for arithmetic non-negative random variables. Such a model is defined through a univariate survival function that is shown to be n-monotone. Two general representations are obtained, by conditioning on the sum of the n variables or through a doubly mixed multinomial distribution. Several other properties including correlation measures are derived. Three processes in insurance theory are discussed for which the claim interarrival periods form a Schur-constant model

Partially Schur-constant models

In this paper, we introduce a new multivariate dependence model that generalizes the standard Schur-constant model. The difference is that the random vector considered is partially exchangeable, instead of exchangeable, whence the term partially Schur-constant. Its advantage is to allow some heterogeneity of marginal distributions and a more flexible dependence structure, which broadens the scope of potential applications. We first show that the associated joint survival function is a monotonic multivariate function. Next, we derive two distributional representations that provide an intuitive understanding of the underlying dependence. Several other properties are obtained, including correlations within and between subvectors. As an illustration, we explain how such a model could be applied to risk management for insurance networks

Instruments d’observació ad hoc per a l’anàlisi de les accions motrius en Dansa Contemporània, Expressió Corporal i Dansa Contact-Improvisation

La Dansa i l’Expressió Corporal són disciplines que promouen la contínua generació d’accions motrius diverses i singularitzades i és per això que es reclama la creació de sistemes de categories específics per a la seva observació i anàlisi. En aquest article exposem tres estudis que ens han permès d’elaborar, mitjançant la metodologia observacional, tres sistemes de categories d’una manera progressiva i ad hoc a aquestes disciplines. Tots tres formen part d’una investigació institucional de l’AGAUR (INEFCP). Si l’objecte d’estudi és la capacitat de generar respostes motrius singularitzades, les dimensions, segons l’especificitat de cada sistema, es troben estructurades des de tres nivells d’anàlisi: el primer, en relació a les fases de tot procés creatiu (Guildford, 1970); el segon, en relació a les habilitats motrius a partir del sistema d’observació OSMOS (Castañer, Torrents, Dinušová, Anguera, 2008), i, el tercer, en relació a les dimensions dels contexts naturals (Anguera, 2005) i, en concret, de la Dansa (Laban, 1988). La codificació s’ha realitzat mitjançant el programari Match Vision Studio (Perea, Ezpeleta, Castellano, 2004)