La seguente tesi e’ costituita da tre diversi elaborati, il primo e’ l’estensione di un modello di equilibrio generale a due regioni (Benigno JIE 2004) con l’intento di calcolare i pesi ottimali per l’inflazione dell’area euro utilizzando micro dati sull’eterogeneità delle rigidità dei prezzi in Europa. Il secondo e il terzo elaborato si focalizzano invece sulle crisi d’insolvenza con l’obiettivo di selezionare le variabili che forniscono maggiori informazioni per la previsione della crisi. La metodologia utilizzata e’ l’analisi della transvariazione. Mentre il secondo ‘essay’ si concentra sulla versione univariata, il terzo estende la metodologia al caso multivariato. Il primo analizza le crisi d’insolvenza più severe degli anni ’90, la seconda utilizza invece gli episodi di crisi analizzati da Frankel e Rose (1996). / The present work is made of three different essays, the first is an extension of a two region general equilibrium model (Benigno JIE 2004), with the intent of calculating optimal weights for EU inflation using micro data on the level of price rigidities, the second and the third have as main focus financial and currency country crises, with the task of selecting the most important variables in terms of crisis prediction by means of a descriptive statistics methodology called transvariation analysis. While the second essay focuses on univariate transvariation, the third extends the methodology to a multivariate framework. The last two essays are based on two different datasets. The first studies the most recent deep financial crises of the 1990s and the source is IMF, International Financial Statistics, the second uses a vast sample of currency crisis episodes taken from Frankel and Rose (1996) dataset made of annual data on more than one hundred developed countries from 1971 through 1992 and defining currency crash as a large change of nominal exchange rate that is also a substantial increase in the rate of change of nominal depreciation. The source in this case is World Bank, World Development Indicators.

Cette thèse se compose de plusieurs travaux portant sur l'énumération et le comportement asymptotique de structures combinatoires apparentées aux partitions d'entiers. Un premier travail s'intéresse aux partitions d'entiers bipartites, qui constituent une généralisation bidimensionnelle des partitions d'entiers. Des équivalents du nombre de partitions sont obtenus dans le régime critique où l'un des entiers est de l'ordre du carré de l'autre entier et au delà de ce régime critique. Ceci complète les résultats établis dans les années cinquante par Auluck, Nanda et Wright. Le deuxième travail traite des chaînes polygonales à sommets entiers dans le plan. Pour un modèle statistique introduit par Sinaï, une représentation intégrale exacte de la fonction de partition est donnée. Ceci conduit à un équivalent du nombre de chaînes joignant deux points distants qui fait intervenir les zéros non triviaux de la fonction zêta de Riemann. Une analyse combinatoire détaillée des chaînes convexes est présentée. Elle permet de montrer l'existence d'une forme limite pour les chaînes convexes aléatoires ayant peu de sommets, répondant ainsi à une question ouverte de Vershik. Un troisième travail porte sur les zonotopes à sommets entiers en dimension supérieure. Un équivalent simple est donné pour le logarithme du nombre de zonotopes contenus dans un cône convexe et dont les extrémités sont fixées. Une loi des grands nombres est établie et la forme limite est caractérisée par la transformée de Laplace du cône. / This thesis consists of several works dealing with the enumeration and the asymptotic behaviour of combinatorial structures related to integer partitions. A first work concerns partitions of large bipartite integers, which are a bidimensional generalization of integer partitions. Asymptotic formulæ are obtained in the critical regime where one of the numbers is of the order of magnitude of the square of the other number, and beyond this critical regime. This completes the results established in the fifties by Auluck, Nanda, and Wright. The second work deals with lattice convex chains in the plane. In a statistical model introduced by Sinaï, an exact integral representation of the partition function is given. This leads to an asymptotic formula for the number of chains joining two distant points, which involves the non trivial zeros of the Riemann zeta function. A detailed combinatorial analysis of convex chains is presented. It makes it possible to prove the existence of a limit shape for random convex chains with few vertices, answering an open question of Vershik. A third work focuses on lattice zonotopes in higher dimensions. An asymptotic equality is given for the logarithm of the number of zonotopes contained in a convex cone and such that the endings of the zonotope are fixed. A law of large numbers is established and the limit shape is characterized by the Laplace transform of the cone.