An Introduction to parametric and non-parametric models for bivariate positive insurance claim severity distributions

We present a real data set of claims amounts where costs related to damage are recorded separately from those related to medical expenses. Only claims with positive costs are considered here. Two approaches to density estimation are presented: a classical parametric and a semi-parametric method, based on transformation kernel density estimation. We explore the data set with standard univariate methods. We also propose ways to select the bandwidth and transformation parameters in the univariate case based on Bayesian methods. We indicate how to compare the results of alternative methods both looking at the shape of the overall density domain and exploring the density estimates in the right tail.

A well-posedness theory in measures for some kinetic models of collective motion

We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the behavior of large groups of animals, such as flocks of birds, swarms, or schools of fish. Our aim is to give a well-posedness theory for general models which possibly include a variety of effects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging effect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and self-propulsion effects, which take into account effects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models.

Modelling dependence in a ratemaking procedure with multivariate Poisson regression models

When actuaries face with the problem of pricing an insurance contract that contains different types of coverage, such as a motor insurance or homeowner's insurance policy, they usually assume that types of claim are independent. However, this assumption may not be realistic: several studies have shown that there is a positive correlation between types of claim. Here we introduce different regression models in order to relax the independence assumption, including zero-inflated models to account for excess of zeros and overdispersion. These models have been largely ignored to multivariate Poisson date, mainly because of their computational di±culties. Bayesian inference based on MCMC helps to solve this problem (and also lets us derive, for several quantities of interest, posterior summaries to account for uncertainty). Finally, these models are applied to an automobile insurance claims database with three different types of claims. We analyse the consequences for pure and loaded premiums when the independence assumption is relaxed by using different multivariate Poisson regression models and their zero-inflated versions.

Interactive Epistemology and Reasoning: On the Foundations of Game Theory

Game theory describes and analyzes strategic interaction. It is usually distinguished between static games, which are strategic situations in which the players choose only once as well as simultaneously, and dynamic games, which are strategic situations involving sequential choices. In addition, dynamic games can be further classified according to perfect and imperfect information. Indeed, a dynamic game is said to exhibit perfect information, whenever at any point of the game every player has full informational access to all choices that have been conducted so far. However, in the case of imperfect information some players are not fully informed about some choices. Game-theoretic analysis proceeds in two steps. Firstly, games are modelled by so-called form structures which extract and formalize the significant parts of the underlying strategic interaction. The basic and most commonly used models of games are the normal form, which rather sparsely describes a game merely in terms of the players' strategy sets and utilities, and the extensive form, which models a game in a more detailed way as a tree. In fact, it is standard to formalize static games with the normal form and dynamic games with the extensive form. Secondly, solution concepts are developed to solve models of games in the sense of identifying the choices that should be taken by rational players. Indeed, the ultimate objective of the classical approach to game theory, which is of normative character, is the development of a solution concept that is capable of identifying a unique choice for every player in an arbitrary game. However, given the large variety of games, it is not at all certain whether it is possible to device a solution concept with such universal capability. Alternatively, interactive epistemology provides an epistemic approach to game theory of descriptive character. This rather recent discipline analyzes the relation between knowledge, belief and choice of game-playing agents in an epistemic framework. The description of the players' choices in a given game relative to various epistemic assumptions constitutes the fundamental problem addressed by an epistemic approach to game theory. In a general sense, the objective of interactive epistemology consists in characterizing existing game-theoretic solution concepts in terms of epistemic assumptions as well as in proposing novel solution concepts by studying the game-theoretic implications of refined or new epistemic hypotheses. Intuitively, an epistemic model of a game can be interpreted as representing the reasoning of the players. Indeed, before making a decision in a game, the players reason about the game and their respective opponents, given their knowledge and beliefs. Precisely these epistemic mental states on which players base their decisions are explicitly expressible in an epistemic framework. In this PhD thesis, we consider an epistemic approach to game theory from a foundational point of view. In Chapter 1, basic game-theoretic notions as well as Aumann's epistemic framework for games are expounded and illustrated. Also, Aumann's sufficient conditions for backward induction are presented and his conceptual views discussed. In Chapter 2, Aumann's interactive epistemology is conceptually analyzed. In Chapter 3, which is based on joint work with Conrad Heilmann, a three-stage account for dynamic games is introduced and a type-based epistemic model is extended with a notion of agent connectedness. Then, sufficient conditions for backward induction are derived. In Chapter 4, which is based on joint work with Jérémie Cabessa, a topological approach to interactive epistemology is initiated. In particular, the epistemic-topological operator limit knowledge is defined and some implications for games considered. In Chapter 5, which is based on joint work with Jérémie Cabessa and Andrés Perea, Aumann's impossibility theorem on agreeing to disagree is revisited and weakened in the sense that possible contexts are provided in which agents can indeed agree to disagree.

Estimation of dynamic latent variable models using simulated nonparametric moments

Abstract. Given a model that can be simulated, conditional moments at a trial parameter value can be calculated with high accuracy by applying kernel smoothing methods to a long simulation. With such conditional moments in hand, standard method of moments techniques can be used to estimate the parameter. Because conditional moments are calculated using kernel smoothing rather than simple averaging, it is not necessary that the model be simulable subject to the conditioning information that is used to define the moment conditions. For this reason, the proposed estimator is applicable to general dynamic latent variable models. It is shown that as the number of simulations diverges, the estimator is consistent and a higher-order expansion reveals the stochastic difference between the infeasible GMM estimator based on the same moment conditions and the simulated version. In particular, we show how to adjust standard errors to account for the simulations. Monte Carlo results show how the estimator may be applied to a range of dynamic latent variable (DLV) models, and that it performs well in comparison to several other estimators that have been proposed for DLV models.

The gamma-crystallins and human cataracts: a puzzle made clearer.

Despite the fact that cataracts constitute the leading cause of blindness worldwide, the mechanisms of lens opacification remain unclear. We recently mapped the aculeiform cataract to the gamma-crystallin locus (CRYG) on chromosome 2q33-35, and mutational analysis of the CRYG-genes cluster identified the aculeiform-cataract mutation in exon 2 of gamma-crystallin D (CRYGD). This mutation occurred in a highly conserved amino acid and could be associated with an impaired folding of CRYGD. During our study, we observed that the previously reported Coppock-like-cataract mutation, the first human cataract mutation, in the pseudogene CRYGE represented a polymorphism seen in 23% of our control population. Further analysis of the original Coppock-like-cataract family identified a missense mutation in a highly conserved segment of exon 2 of CRYGC. These mutations were not seen in a large control population. There is no direct evidence, to date, that up-regulation of a pseudogene causes cataracts. To our knowledge, these findings are the first evidence of an involvement of CRYGC and support the role of CRYGD in human cataract formation.

Theoretical aspects of graph models for MANETs

We survey the main theoretical aspects of models for Mobile Ad Hoc Networks (MANETs). We present theoretical characterizations of mobile network structural properties, different dynamic graph models of MANETs, and finally we give detailed summaries of a few selected articles. In particular, we focus on articles dealing with connectivity of mobile networks, and on articles which show that mobility can be used to propagate information between nodes of the network while at the same time maintaining small transmission distances, and thus saving energy.

Ichthyosen : Pathophysiologische Modelle der epidermalen Differenzierung [The ichthyoses : Pathophysiological models of epidermal differentiation].

The ichthyoses are a heterogeneous group of monogenetically inherited disorders of cornification, and characterized clinically by scaling or hyperkeratosis. Historically, they were classified by clinical features and inheritance patterns. As a result of the recent molecular biological revolution, the ichthyoses are now recognized as comprising many diverse entities. Importantly, identical phenotypes may be caused by mutations in multiple genes, while mutations in a single gene may result in multiple and sometimes widely divergent phenotypes. The considerable complexity of this clinically and genetically heterogeneous group of disorders has prompted the need for a new classification. A classification that uses terminology based on a combination of the clinical and molecular genetic details, for instance loricrin keratoderma, is desirable. In this chapter we will use in principle the nosology adopted recently by an international group of experts at the First Ichthyosis Consensus Conference in Sorèz, France.

Towards the validation of "in silico" models and physicochemical filters to identify and characterize new chemical entities

Summary: Lipophilicity plays an important role in the determination and the comprehension of the pharmacokinetic behavior of drugs. It is usually expressed by the partition coefficient (log P) in the n-octanol/water system. The use of an additional solvent system (1,2-dichlorethane/water) is necessary to obtain complementary information, as the log Poct values alone are not sufficient to explain ail biological properties. The aim of this thesis is to develop tools allowing to predict lipophilicity of new drugs and to analyze the information yielded by those log P values. Part I presents the development of theoretical models used to predict lipophilicity. Chapter 2 shows the necessity to extend the existing solvatochromic analyses in order to predict correctly the lipophilicity of new and complex neutral compounds. In Chapter 3, solvatochromic analyses are used to develop a model for the prediction of the lipophilicity of ions. A global model was obtained allowing to estimate the lipophilicity of neutral, anionic and cationic solutes. Part II presents the detailed study of two physicochemical filters. Chapter 4 shows that the Discovery RP Amide C16 stationary phase allows to estimate lipophilicity of the neutral form of basic and acidic solutes, except of lipophilic acidic solutes. Those solutes present additional interactions with this particular stationary phase. In Chapter 5, 4 different IANI stationary phases are investigated. For neutral solutes, linear data are obtained whatever the IANI column used. For the ionized solutes, their retention is due to a balance of electrostatic and hydrophobie interactions. Thus no discrimination is observed between different series of solutes bearing the same charge, from one column to an other. Part III presents two examples illustrating the information obtained thanks to Structure-Properties Relationships (SPR). Comparing graphically lipophilicity values obtained in two different solvent systems allows to reveal the presence of intramolecular effects .such as internai H-bond (Chapter 6). SPR is used to study the partitioning of ionizable groups encountered in Medicinal Chemistry (Chapter7). Résumé La lipophilie joue un .rôle important dans la détermination et la compréhension du comportement pharmacocinétique des médicaments. Elle est généralement exprimée par le coefficient de partage (log P) d'un composé dans le système de solvants n-octanol/eau. L'utilisation d'un deuxième système de solvants (1,2-dichloroéthane/eau) s'est avérée nécessaire afin d'obtenir des informations complémentaires, les valeurs de log Poct seules n'étant pas suffisantes pour expliquer toutes les propriétés biologiques. Le but de cette thèse est de développer des outils permettant de prédire la lipophilie de nouveaux candidats médicaments et d'analyser l'information fournie par les valeurs de log P. La Partie I présente le développement de modèles théoriques utilisés pour prédire la lipophilie. Le chapitre 2 montre la nécessité de mettre à jour les analyses solvatochromiques existantes mais inadaptées à la prédiction de la lipophilie de nouveaux composés neutres. Dans le chapitre 3, la même méthodologie des analyses solvatochromiques est utilisée pour développer un modèle permettant de prédire la lipophilie des ions. Le modèle global obtenu permet la prédiction de la lipophilie de composés neutres, anioniques et cationiques. La Partie II présente l'étude approfondie de deux filtres physicochimiques. Le Chapitre 4 montre que la phase stationnaire Discovery RP Amide C16 permet la détermination de la lipophilie de la forme neutre de composés basiques et acides, à l'exception des acides très lipophiles. Ces derniers présentent des interactions supplémentaires avec cette phase stationnaire. Dans le Chapitre 5, 4 phases stationnaires IAM sont étudiées. Pour les composés neutres étudiés, des valeurs de rétention linéaires sont obtenues, quelque que soit la colonne IAM utilisée. Pour les composés ionisables, leur rétention est due à une balance entre des interactions électrostatiques et hydrophobes. Donc aucune discrimination n'est observée entre les différentes séries de composés portant la même charge d'une colonne à l'autre. La Partie III présente deux exemples illustrant les informations obtenues par l'utilisation des relations structures-propriétés. Comparer graphiquement la lipophilie mesurée dans deux différents systèmes de solvants permet de mettre en évidence la présence d'effets intramoléculaires tels que les liaisons hydrogène intramoléculaires (Chapitre 6). Cette approche des relations structures-propriétés est aussi appliquée à l'étude du partage de fonctions ionisables rencontrées en Chimie Thérapeutique (Chapitre 7) Résumé large public Pour exercer son effet thérapeutique, un médicament doit atteindre son site d'action en quantité suffisante. La quantité effective de médicament atteignant le site d'action dépend du nombre d'interactions entre le médicament et de nombreux constituants de l'organisme comme, par exemple, les enzymes du métabolisme ou les membranes biologiques. Le passage du médicament à travers ces membranes, appelé perméation, est un paramètre important à optimiser pour développer des médicaments plus puissants. La lipophilie joue un rôle clé dans la compréhension de la perméation passive des médicaments. La lipophilie est généralement exprimée par le coefficient de partage (log P) dans le système de solvants (non miscibles) n-octanol/eau. Les valeurs de log Poct seules se sont avérées insuffisantes pour expliquer la perméation à travers toutes les différentes membranes biologiques du corps humain. L'utilisation d'un système de solvants additionnel (le système 1,2-dichloroéthane/eau) a permis d'obtenir les informations complémentaires indispensables à une bonne compréhension du processus de perméation. Un grand nombre d'outils expérimentaux et théoriques sont à disposition pour étudier la lipophilie. Ce travail de thèse se focalise principalement sur le développement ou l'amélioration de certains de ces outils pour permettre leur application à un champ plus large de composés. Voici une brève description de deux de ces outils: 1)La factorisation de la lipophilie en fonction de certaines propriétés structurelles (telle que le volume) propres aux composés permet de développer des modèles théoriques utilisables pour la prédiction de la lipophilie de nouveaux composés ou médicaments. Cette approche est appliquée à l'analyse de la lipophilie de composés neutres ainsi qu'à la lipophilie de composés chargés. 2)La chromatographie liquide à haute pression sur phase inverse (RP-HPLC) est une méthode couramment utilisée pour la détermination expérimentale des valeurs de log Poct.

Multivariate contemporaneous-threshold autoregressive models

This paper proposes a contemporaneous-threshold multivariate smooth transition autoregressive (C-MSTAR) model in which the regime weights depend on the ex ante probabilities that latent regime-specific variables exceed certain threshold values. A key feature of the model is that the transition function depends on all the parameters of the model as well as on the data. Since the mixing weights are also a function of the regime-specific innovation covariance matrix, the model can account for contemporaneous regime-specific co-movements of the variables. The stability and distributional properties of the proposed model are discussed, as well as issues of estimation, testing and forecasting. The practical usefulness of the C-MSTAR model is illustrated by examining the relationship between US stock prices and interest rates.

State-dependent threshold STAR models

In this paper we consider extensions of smooth transition autoregressive (STAR) models to situations where the threshold is a time-varying function of variables that affect the separation of regimes of the time series under consideration. Our specification is motivated by the observation that unusually high/low values for an economic variable may sometimes be best thought of in relative terms. State-dependent logistic STAR and contemporaneous-threshold STAR models are introduced and discussed. These models are also used to investigate the dynamics of U.S. short-term interest rates, where the threshold is allowed to be a function of past output growth and inflation.

A comparison of input-output models: ghosh reduces to leontief (but "closing" ghosh makes it more plausible)

Ghosh's model is discussed in this paper under two alternative scenarios. In an open version we compare it with Leontief's model and prove that they reduce to each other under some specific productive conditions. We then move onto reconsidering Ghosh's model alleged implausibility and we do so reformulating the model to incorporate a closure rule. The closure solves, to some extent, the implausibility problem very clearly put out by Oosterhaven for then value-added is correctly computed and responsive to allocation changes resulting from supply shocks.

Chimpanzees and supporting models in the study of malaria pre-erythrocytic stages

Chimpanzees are being used in the study of immune response to Plasmodium falciparum malaria pre-erythrocytic stages (MPES). Responses induced by immunisation with recombinant/synthetic antigens and by irradiated sporozoites are being evaluated in a model system that is phylogenetically close to humans and that is amenable to limited manipulation not possible in humans. The value of chimpanzees for the in-depth study of immunological mechanisms at work in MPES-induced protection are discussed. A total number of 7 chimpanzees have been used to evaluate the immune response to recombinant antigens, and 5 have been challenged with large numbers of sporozoites, followed by surgical liver-wedge resection, in order to generate infected liver tissue for histological and immunological studies. As a complementary model, SCID mice carrying live, transplanted human and primate hepatocytes have been inoculated with sporozoites and infection of transplanted cells has been monitored by histological and immunological methods. In ongoing experiments chimpanzees are being immunised with MPES-derived lipopeptides that have been shown to overcome MHC restriction in mice, and with irradiated sporozoites.