Well-posedness and invariant measures for HJM models with deterministic volatility and Lévy noise

We give sufficient conditions for existence, uniqueness and ergodicity of invariant measures for Musiela's stochastic partial differential equation with deterministic volatility and a Hilbert space valued driving Lévy noise. Conditions for the absence of arbitrage and for the existence of mild solutions are also discussed.

Estimation of dynamic latent variable models using simulated nonparametric moments

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. Since 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. Monte Carlo results show that the estimator performs well in comparison to other estimators that have been proposed for estimation of general DLV models.

Generalized factor models: a bayesian approach

There is recent interest in the generalization of classical factor models in which the idiosyncratic factors are assumed to be orthogonal and there are identification restrictions on cross-sectional and time dimensions. In this study, we describe and implement a Bayesian approach to generalized factor models. A flexible framework is developed to determine the variations attributed to common and idiosyncratic factors. We also propose a unique methodology to select the (generalized) factor model that best fits a given set of data. Applying the proposed methodology to the simulated data and the foreign exchange rate data, we provide a comparative analysis between the classical and generalized factor models. We find that when there is a shift from classical to generalized, there are significant changes in the estimates of the structures of the covariance and correlation matrices while there are less dramatic changes in the estimates of the factor loadings and the variation attributed to common factors.

Caracteritació de models funcionals d'àmfores romanes mitjançant Finite Element Analysis

Projecte de recerca elaborat a partir d’una estada al Laboratory of Archaeometry del National Centre of Scientific Research “Demokritos” d’Atenes, Grècia, entre juny i setembre 2006. Aquest estudi s’emmarca dins d’un context més ampli d’estudi del canvi tecnològic que es documenta en la producció d’àmfores de tipologia romana durant els segles I aC i I dC en els territoris costaners de Catalunya. Una part d’aquest estudi contempla el càlcul de les propietats mecàniques d’aquestes àmfores i la seva avaluació en funció de la tipologia amforal, a partir de l’Anàlisi d’Elements Finits (AEF). L’AEF és una aproximació numèrica que té el seu origen en les ciències d’enginyeria i que ha estat emprada per estimar el comportament mecànic d’un model en termes, per exemple, de deformació i estrès. Així, un objecte, o millor dit el seu model, es dividit en sub-dominis anomenats elements finits, als quals se’ls atribueixen les propietats mecàniques del material en estudi. Aquests elements finits estan connectats formant una xarxa amb constriccions que pot ser definida. En el cas d’aplicar una força determinada a un model, el comportament de l’objecte pot ser estimat mitjançant el conjunt d’equacions lineals que defineixen el rendiment dels elements finits, proporcionant una bona aproximació per a la descripció de la deformació estructural. Així, aquesta simulació per ordinador suposa una important eina per entendre la funcionalitat de ceràmiques arqueològiques. Aquest procediment representa un model quantitatiu per predir el trencament de l’objecte ceràmic quan aquest és sotmès a diferents condicions de pressió. Aquest model ha estat aplicat a diferents tipologies amforals. Els resultats preliminars mostren diferències significatives entre la tipologia pre-romana i les tipologies romanes, així com entre els mateixos dissenys amforals romans, d’importants implicacions arqueològiques.

A general construction of internal sheaves in algebraic set theory

We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothen-dieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.

A priori ratemaking using bivariate poisson regression models

In automobile insurance, it is useful to achieve a priori ratemaking by resorting to gene- ralized linear models, and here the Poisson regression model constitutes the most widely accepted basis. However, insurance companies distinguish between claims with or without bodily injuries, or claims with full or partial liability of the insured driver. This paper exa- mines an a priori ratemaking procedure when including two di®erent types of claim. When assuming independence between claim types, the premium can be obtained by summing the premiums for each type of guarantee and is dependent on the rating factors chosen. If the independence assumption is relaxed, then it is unclear as to how the tari® system might be a®ected. In order to answer this question, bivariate Poisson regression models, suitable for paired count data exhibiting correlation, are introduced. It is shown that the usual independence assumption is unrealistic here. These models are applied to an automobile insurance claims database containing 80,994 contracts belonging to a Spanish insurance company. Finally, the consequences for pure and loaded premiums when the independence assumption is relaxed by using a bivariate Poisson regression model are analysed.

Models i formes de la pintura catalana del Barroc: el mirall de l'art francès

Estudi elaborat a partir d’una estada a l’Institut National d'Histoire de l'Art- Bibliothèque Nationale de France entre l'1 i el 31 de juliol de 2007. S’ha treballat en la recerca documental sobre les relacions artístiques entre França i Catalunya a l’Època Moderna. Els materials o fons documentals d’interès han estat dos: els fons gràfics d’estampes i gravats de la Bibliothèque Nationale, no tant en el sentit de consulta dels originals –que en alguna ocasió també- com sí en el la visualització de les vastíssimes fototeques, que ha permès a l’autor aplegar un bon nombre d’imatges que en el futur serviran per posar en relació la cultura figurativa francesa –sobretot de la pintura i de l’escultura, però també de la tractadística arquitectònica- amb la catalana de l’època, ja sigui per constatar les semblances com per fer notar les diferències en els usos dels models figuratius. S’ha buidat material bibliogràfic difícil de localitzar a Catalunya. Són publicacions referides a gravat, d’una banda, i a patrimoni artístic. Aquest darrer aspecte s’ha treballat des de dos vessants: en seguir notícies de la presència d’artistes catalans a França i viceversa, i en buscar dades sobre l’espoli d’obres d’art portat a terme a Catalunya durant el període napoleònic.

Two different 3D biogeochemical models for the NW mediterranean sea: validation with Meris data and intercomparison

Report for the scientific sojourn carried out at the University of New South Wales from February to June the 2007. Two different biogeochemical models are coupled to a three dimensional configuration of the Princeton Ocean Model (POM) for the Northwestern Mediterranean Sea (Ahumada and Cruzado, 2007). The first biogeochemical model (BLANES) is the three-dimensional version of the model described by Bahamon and Cruzado (2003) and computes the nitrogen fluxes through six compartments using semi-empirical descriptions of biological processes. The second biogeochemical model (BIOMEC) is the biomechanical NPZD model described in Baird et al. (2004), which uses a combination of physiological and physical descriptions to quantify the rates of planktonic interactions. Physical descriptions include, for example, the diffusion of nutrients to phytoplankton cells and the encounter rate of predators and prey. The link between physical and biogeochemical processes in both models is expressed by the advection-diffusion of the non-conservative tracers. The similarities in the mathematical formulation of the biogeochemical processes in the two models are exploited to determine the parameter set for the biomechanical model that best fits the parameter set used in the first model. Three years of integration have been carried out for each model to reach the so called perpetual year run for biogeochemical conditions. Outputs from both models are averaged monthly and then compared to remote sensing images obtained from sensor MERIS for chlorophyll.

Models de simulació per coordinar serveis d'emergència

El projecte exposat té com a propòsit definir i implementar un model de simulació basat en la coordinació i assignació dels serveis d’emergència en accidents de trànsit. La definició del model s’ha realitzat amb l’ús de les Xarxes de Petri Acolorides i la implementació amb el software Rockwell Arena 7.0. El modelatge de la primera simulació ens mostra un model teòric basat en cues mentre que el segon, mostra un model més complet i real gràcies a la connexió mitjançant la plataforma Corba a una base de dades amb informació geogràfica de les flotes i de les rutes. Com a resultat de l’estudi i amb l’ajuda de GoogleEarth, podem realitzar simulacions gràfiques per veure els accidents generats, les flotes dels serveis i el moviment dels vehicles des de les bases fins als accidents.

Expansió accelerada de l’univers i teories de gravetat modificada a grans escales

Estudi realitzat a partir d’una estada al Physics Department de la New York University, United States, Estats Units, entre 2006 i 2008. Una de les observacions de més impacte en la cosmologia moderna ha estat la determinació empírica que l’Univers es troba actualment en una fase d’Expansió Accelerada (EA). Aquest fenòmen implica que o bé l’Univers està dominat per un nou sector de matèria/energia, o bé la Relativitat General deixa de tenir validesa a escales cosmològiques. La primera possibilitat comprèn els models d’Energia Fosca (EF), i el seu principal problema és que l’EF ha de tenir propietats tan especials que es fan difícils de justificar teòricament. La segona possibilitat requereix la construcció de teories consistents de Gravetat Modificada a Grans Distàncies (GMGD), que són una generalització dels models de gravetat massiva. L’interès fenomenològic per aquestes teories també va resorgir amb l’aparició dels primers exemples de models de GMGD, com ara el model de Dvali, Gabadadze i Porrati (DGP), que consisteix en un tipus de brana en una dimensió extra. Malauradament, però, aquest model no permet explicar de forma consistent l’EA de l’Univers. Un dels objectius d’aquest projecte ha estat establir la viabilitat interna i fenomenològica dels models de GMGD. Des del punt de vista fenomenològic, ens hem centrat en la questió més important a la pràctica: trobar signatures observacionals que permetin distingir els models de GMGD dels d’EF. A nivell més teòric, també hem investigat el significat de les inestabilitats del model DGP.L’altre gran objectiu que ens vam proposar va ser la construcció de noves teories de GMGD. En la segona part d’aquest projecte, hem elaborat i mostrat la consistència del model “DGP en Cascada”, que generalitza el model DGP a més dimensions extra, i representa el segon model consistent i invariant-Lorentz a l’espai pla conegut. L’existència d’altres models de GMGD més enllà de DGP és de gran interès atès que podria permetre obtenir l’EA de l’Univers de forma purament geomètrica.

Structured and unstructured continuous models for Wolbachia infections

We introduce and investigate a series of models for an infection of a diplodiploid host species by the bacterial endosymbiont Wolbachia. The continuous models are characterized by partial vertical transmission, cytoplasmic incompatibility and fitness costs associated with the infection. A particular aspect of interest is competitions between mutually incompatible strains. We further introduce an age-structured model that takes into account different fertility and mortality rates at different stages of the life cycle of the individuals. With only a few parameters, the ordinary differential equation models exhibit already interesting dynamics and can be used to predict criteria under which a strain of bacteria is able to invade a population. Interestingly, but not surprisingly, the age-structured model shows significant differences concerning the existence and stability of equilibrium solutions compared to the unstructured model.

The role of fixed delays in neuronal rate models

Fixed delays in neuronal interactions arise through synaptic and dendritic processing. Previous work has shown that such delays, which play an important role in shaping the dynamics of networks of large numbers of spiking neurons with continuous synaptic kinetics, can be taken into account with a rate model through the addition of an explicit, fixed delay. Here we extend this work to account for arbitrary symmetric patterns of synaptic connectivity and generic nonlinear transfer functions. Specifically, we conduct a weakly nonlinear analysis of the dynamical states arising via primary instabilities of the stationary uniform state. In this way we determine analytically how the nature and stability of these states depend on the choice of transfer function and connectivity. While this dependence is, in general, nontrivial, we make use of the smallness of the ratio in the delay in neuronal interactions to the effective time constant of integration to arrive at two general observations of physiological relevance. These are: 1 - fast oscillations are always supercritical for realistic transfer functions. 2 - Traveling waves are preferred over standing waves given plausible patterns of local connectivity.

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.