Discrete analysis of dividend payments in a non-life insurance portfolio

The process of free reserves in a non-life insurance portfolio as defined in the classical model of risk theory is modified by the introduction of dividend policies that set maximum levels for the accumulation of reserves. The first part of the work formulates the quantification of the dividend payments via the expectation of their current value under diferent hypotheses. The second part presents a solution based on a system of linear equations for discrete dividend payments in the case of a constant dividend barrier, illustrated by solving a specific case.

Retaining principal components for discrete variables

The present study discusses retention criteria for principal components analysis (PCA) applied to Likert scale items typical in psychological questionnaires. The main aim is to recommend applied researchers to restrain from relying only on the eigenvalue-than-one criterion; alternative procedures are suggested for adjusting for sampling error. An additional objective is to add evidence on the consequences of applying this rule when PCA is used with discrete variables. The experimental conditions were studied by means of Monte Carlo sampling including several sample sizes, different number of variables and answer alternatives, and four non-normal distributions. The results suggest that even when all the items and thus the underlying dimensions are independent, eigenvalues greater than one are frequent and they can explain up to 80% of the variance in data, meeting the empirical criterion. The consequences of using Kaiser"s rule are illustrated with a clinical psychology example. The size of the eigenvalues resulted to be a function of the sample size and the number of variables, which is also the case for parallel analysis as previous research shows. To enhance the application of alternative criteria, an R package was developed for deciding the number of principal components to retain by means of confidence intervals constructed about the eigenvalues corresponding to lack of relationship between discrete variables.

Applications of Fourier transform infrared spectroscopy

This article summarizes the basic principles of Fourier Transform Infrared Spectroscopy, with examples of methodologies and applications to different field sciences.

On the tractability of the piecewise-linear approximation for general discrete-choice network revenue management

The choice network revenue management (RM) model incorporates customer purchase behavioras customers purchasing products with certain probabilities that are a function of the offeredassortment of products, and is the appropriate model for airline and hotel network revenuemanagement, dynamic sales of bundles, and dynamic assortment optimization. The underlyingstochastic dynamic program is intractable and even its certainty-equivalence approximation, inthe form of a linear program called Choice Deterministic Linear Program (CDLP) is difficultto solve in most cases. The separation problem for CDLP is NP-complete for MNL with justtwo segments when their consideration sets overlap; the affine approximation of the dynamicprogram is NP-complete for even a single-segment MNL. This is in contrast to the independentclass(perfect-segmentation) case where even the piecewise-linear approximation has been shownto be tractable. In this paper we investigate the piecewise-linear approximation for network RMunder a general discrete-choice model of demand. We show that the gap between the CDLP andthe piecewise-linear bounds is within a factor of at most 2. We then show that the piecewiselinearapproximation is polynomially-time solvable for a fixed consideration set size, bringing itinto the realm of tractability for small consideration sets; small consideration sets are a reasonablemodeling tradeoff in many practical applications. Our solution relies on showing that forany discrete-choice model the separation problem for the linear program of the piecewise-linearapproximation can be solved exactly by a Lagrangian relaxation. We give modeling extensionsand show by numerical experiments the improvements from using piecewise-linear approximationfunctions.

Evolutionarily stable learning schedules and cumulative culture in discrete generation models.

Individual learning (e.g., trial-and-error) and social learning (e.g., imitation) are alternative ways of acquiring and expressing the appropriate phenotype in an environment. The optimal choice between using individual learning and/or social learning may be dictated by the life-stage or age of an organism. Of special interest is a learning schedule in which social learning precedes individual learning, because such a schedule is apparently a necessary condition for cumulative culture. Assuming two obligatory learning stages per discrete generation, we obtain the evolutionarily stable learning schedules for the three situations where the environment is constant, fluctuates between generations, or fluctuates within generations. During each learning stage, we assume that an organism may target the optimal phenotype in the current environment by individual learning, and/or the mature phenotype of the previous generation by oblique social learning. In the absence of exogenous costs to learning, the evolutionarily stable learning schedules are predicted to be either pure social learning followed by pure individual learning ("bang-bang" control) or pure individual learning at both stages ("flat" control). Moreover, we find for each situation that the evolutionarily stable learning schedule is also the one that optimizes the learned phenotype at equilibrium.

Prediction of Childhood Asthma Using Conditional Probability and Discrete Event Simulation

Abstract: Asthma prevalence in children and adolescents in Spain is 10-17%. It is the most common chronic illness during childhood. Prevalence has been increasing over the last 40 years and there is considerable evidence that, among other factors, continued exposure to cigarette smoke results in asthma in children. No statistical or simulation model exist to forecast the evolution of childhood asthma in Europe. Such a model needs to incorporate the main risk factors that can be managed by medical authorities, such as tobacco (OR = 1.44), to establish how they affect the present generation of children. A simulation model using conditional probability and discrete event simulation for childhood asthma was developed and validated by simulating realistic scenario. The parameters used for the model (input data) were those found in the bibliography, especially those related to the incidence of smoking in Spain. We also used data from a panel of experts from the Hospital del Mar (Barcelona) related to actual evolution and asthma phenotypes. The results obtained from the simulation established a threshold of a 15-20% smoking population for a reduction in the prevalence of asthma. This is still far from the current level in Spain, where 24% of people smoke. We conclude that more effort must be made to combat smoking and other childhood asthma risk factors, in order to significantly reduce the number of cases. Once completed, this simulation methodology can realistically be used to forecast the evolution of childhood asthma as a function of variation in different risk factors.

Fourier transform convolution integrals applied to generalized Born molecular volume.

Generalized Born methods are currently among the solvation models most commonly used for biological applications. We reformulate the generalized Born molecular volume method initially described by (Lee et al, 2003, J Phys Chem, 116, 10606; Lee et al, 2003, J Comp Chem, 24, 1348) using fast Fourier transform convolution integrals. Changes in the initial method are discussed and analyzed. Finally, the method is extensively checked with snapshots from common molecular modeling applications: binding free energy computations and docking. Biologically relevant test systems are chosen, including 855-36091 atoms. It is clearly demonstrated that, precision-wise, the proposed method performs as good as the original, and could better benefit from hardware accelerated boards.

On the inverse windowed Fourier transform

The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the "optimal" solution according to a maximum-entropy selection criterion.

The continuous wavelet transform as a maximum entropy solution of the corresponding inverse problem

The continuous wavelet transform is obtained as a maximumentropy solution of the corresponding inverse problem. It is well knownthat although a signal can be reconstructed from its wavelet transform,the expansion is not unique due to the redundancy of continuous wavelets.Hence, the inverse problem has no unique solution. If we want to recognizeone solution as "optimal", then an appropriate decision criterion hasto be adopted. We show here that the continuous wavelet transform is an"optimal" solution in a maximum entropy sense.

On wideband deconvolution using wavelet transform

A discussion on the expression proposed in [1]–[3]for deconvolving the wideband density function is presented. Weprove here that such an expression reduces to be proportionalto the wideband correlation receiver output, or continuous wavelettransform of the received signal with respect to the transmittedone. Moreover, we show that the same result has been implicitlyassumed in [1], when the deconvolution equation is derived. Westress the fact that the analyzed approach is just the orthogonalprojection of the density function onto the image of the wavelettransform with respect to the transmitted signal. Consequently,the approach can be considered a good representation of thedensity function only under the prior knowledge that the densityfunction belongs to such a subspace. The choice of the transmittedsignal is thus crucial to this approach.

Simulation of stromatolite growth using diffusion-limited aggregation and a discrete model of biogeochemical exchanges in microbial mat

Resume : Mieux comprendre les stromatolithes et les tapis microbiens est un sujet important en biogéosciences puisque cela aide à l'étude des premières formes de vie sur Terre, a mieux cerner l'écologie des communautés microbiennes et la contribution des microorganismes a la biominéralisation, et même à poser certains fondements dans les recherches en exobiologie. D'autre part, la modélisation est un outil puissant utilisé dans les sciences naturelles pour appréhender différents phénomènes de façon théorique. Les modèles sont généralement construits sur un système d'équations différentielles et les résultats sont obtenus en résolvant ce système. Les logiciels disponibles pour implémenter les modèles incluent les logiciels mathématiques et les logiciels généraux de simulation. L'objectif principal de cette thèse est de développer des modèles et des logiciels pour aider a comprendre, via la simulation, le fonctionnement des stromatolithes et des tapis microbiens. Ces logiciels ont été développés en C++ en ne partant d'aucun pré-requis de façon a privilégier performance et flexibilité maximales. Cette démarche permet de construire des modèles bien plus spécifiques et plus appropriés aux phénomènes a modéliser. Premièrement, nous avons étudié la croissance et la morphologie des stromatolithes. Nous avons construit un modèle tridimensionnel fondé sur l'agrégation par diffusion limitée. Le modèle a été implémenté en deux applications C++: un moteur de simulation capable d'exécuter un batch de simulations et de produire des fichiers de résultats, et un outil de visualisation qui permet d'analyser les résultats en trois dimensions. Après avoir vérifié que ce modèle peut en effet reproduire la croissance et la morphologie de plusieurs types de stromatolithes, nous avons introduit un processus de sédimentation comme facteur externe. Ceci nous a mené a des résultats intéressants, et permis de soutenir l'hypothèse que la morphologie des stromatolithes pourrait être le résultat de facteurs externes autant que de facteurs internes. Ceci est important car la classification des stromatolithes est généralement fondée sur leur morphologie, imposant que la forme d'un stromatolithe est dépendante de facteurs internes uniquement (c'est-à-dire les tapis microbiens). Les résultats avancés dans ce mémoire contredisent donc ces assertions communément admises. Ensuite, nous avons décidé de mener des recherches plus en profondeur sur les aspects fonctionnels des tapis microbiens. Nous avons construit un modèle bidimensionnel de réaction-diffusion fondé sur la simulation discrète. Ce modèle a été implémenté dans une application C++ qui permet de paramétrer et exécuter des simulations. Nous avons ensuite pu comparer les résultats de simulation avec des données du monde réel et vérifier que le modèle peut en effet imiter le comportement de certains tapis microbiens. Ainsi, nous avons pu émettre et vérifier des hypothèses sur le fonctionnement de certains tapis microbiens pour nous aider à mieux en comprendre certains aspects, comme la dynamique des éléments, en particulier le soufre et l'oxygène. En conclusion, ce travail a abouti à l'écriture de logiciels dédiés à la simulation de tapis microbiens d'un point de vue tant morphologique que fonctionnel, suivant deux approches différentes, l'une holistique, l'autre plus analytique. Ces logiciels sont gratuits et diffusés sous licence GPL (General Public License). Abstract : Better understanding of stromatolites and microbial mats is an important topic in biogeosciences as it helps studying the early forms of life on Earth, provides clues re- garding the ecology of microbial ecosystems and their contribution to biomineralization, and gives basis to a new science, exobiology. On the other hand, modelling is a powerful tool used in natural sciences for the theoretical approach of various phenomena. Models are usually built on a system of differential equations and results are obtained by solving that system. Available software to implement models includes mathematical solvers and general simulation software. The main objective of this thesis is to develop models and software able to help to understand the functioning of stromatolites and microbial mats. Software was developed in C++ from scratch for maximum performance and flexibility. This allows to build models much more specific to a phenomenon rather than general software. First, we studied stromatolite growth and morphology. We built a three-dimensional model based on diffusion-limited aggregation. The model was implemented in two C++ applications: a simulator engine, which can run a batch of simulations and produce result files, and a Visualization tool, which allows results to be analysed in three dimensions. After verifying that our model can indeed reproduce the growth and morphology of several types of stromatolites, we introduced a sedimentation process as an external factor. This lead to interesting results, and allowed to emit the hypothesis that stromatolite morphology may be the result of external factors as much as internal factors. This is important as stromatolite classification is usually based on their morphology, imposing that a stromatolite shape is dependant on internal factors only (i.e. the microbial mat). This statement is contradicted by our findings, Second, we decided to investigate deeper the functioning of microbial mats, We built a two-dimensional reaction-diffusion model based on discrete simulation, The model was implemented in a C++ application that allows setting and running simulations. We could then compare simulation results with real world data and verify that our model can indeed mimic the behaviour of some microbial mats. Thus, we have proposed and verified hypotheses regarding microbial mats functioning in order to help to better understand them, e.g. the cycle of some elements such as oxygen or sulfur. ln conclusion, this PhD provides a simulation software, dealing with two different approaches. This software is free and available under a GPL licence.