Extremal properties of certain risk models

Cette thèse s'intéresse à étudier les propriétés extrémales de certains modèles de risque d'intérêt dans diverses applications de l'assurance, de la finance et des statistiques. Cette thèse se développe selon deux axes principaux, à savoir: Dans la première partie, nous nous concentrons sur deux modèles de risques univariés, c'est-à- dire, un modèle de risque de déflation et un modèle de risque de réassurance. Nous étudions le développement des queues de distribution sous certaines conditions des risques commun¬s. Les principaux résultats sont ainsi illustrés par des exemples typiques et des simulations numériques. Enfin, les résultats sont appliqués aux domaines des assurances, par exemple, les approximations de Value-at-Risk, d'espérance conditionnelle unilatérale etc. La deuxième partie de cette thèse est consacrée à trois modèles à deux variables: Le premier modèle concerne la censure à deux variables des événements extrême. Pour ce modèle, nous proposons tout d'abord une classe d'estimateurs pour les coefficients de dépendance et la probabilité des queues de distributions. Ces estimateurs sont flexibles en raison d'un paramètre de réglage. Leurs distributions asymptotiques sont obtenues sous certaines condi¬tions lentes bivariées de second ordre. Ensuite, nous donnons quelques exemples et présentons une petite étude de simulations de Monte Carlo, suivie par une application sur un ensemble de données réelles d'assurance. L'objectif de notre deuxième modèle de risque à deux variables est l'étude de coefficients de dépendance des queues de distributions obliques et asymétriques à deux variables. Ces distri¬butions obliques et asymétriques sont largement utiles dans les applications statistiques. Elles sont générées principalement par le mélange moyenne-variance de lois normales et le mélange de lois normales asymétriques d'échelles, qui distinguent la structure de dépendance de queue comme indiqué par nos principaux résultats. Le troisième modèle de risque à deux variables concerne le rapprochement des maxima de séries triangulaires elliptiques obliques. Les résultats théoriques sont fondés sur certaines hypothèses concernant le périmètre aléatoire sous-jacent des queues de distributions. -- This thesis aims to investigate the extremal properties of certain risk models of interest in vari¬ous applications from insurance, finance and statistics. This thesis develops along two principal lines, namely: In the first part, we focus on two univariate risk models, i.e., deflated risk and reinsurance risk models. Therein we investigate their tail expansions under certain tail conditions of the common risks. Our main results are illustrated by some typical examples and numerical simu¬lations as well. Finally, the findings are formulated into some applications in insurance fields, for instance, the approximations of Value-at-Risk, conditional tail expectations etc. The second part of this thesis is devoted to the following three bivariate models: The first model is concerned with bivariate censoring of extreme events. For this model, we first propose a class of estimators for both tail dependence coefficient and tail probability. These estimators are flexible due to a tuning parameter and their asymptotic distributions are obtained under some second order bivariate slowly varying conditions of the model. Then, we give some examples and present a small Monte Carlo simulation study followed by an application on a real-data set from insurance. The objective of our second bivariate risk model is the investigation of tail dependence coefficient of bivariate skew slash distributions. Such skew slash distributions are extensively useful in statistical applications and they are generated mainly by normal mean-variance mixture and scaled skew-normal mixture, which distinguish the tail dependence structure as shown by our principle results. The third bivariate risk model is concerned with the approximation of the component-wise maxima of skew elliptical triangular arrays. The theoretical results are based on certain tail assumptions on the underlying random radius.

The MicroArray Quality Control (MAQC)-II study of common practices for the development and validation of microarray-based predictive models.

Gene expression data from microarrays are being applied to predict preclinical and clinical endpoints, but the reliability of these predictions has not been established. In the MAQC-II project, 36 independent teams analyzed six microarray data sets to generate predictive models for classifying a sample with respect to one of 13 endpoints indicative of lung or liver toxicity in rodents, or of breast cancer, multiple myeloma or neuroblastoma in humans. In total, >30,000 models were built using many combinations of analytical methods. The teams generated predictive models without knowing the biological meaning of some of the endpoints and, to mimic clinical reality, tested the models on data that had not been used for training. We found that model performance depended largely on the endpoint and team proficiency and that different approaches generated models of similar performance. The conclusions and recommendations from MAQC-II should be useful for regulatory agencies, study committees and independent investigators that evaluate methods for global gene expression analysis.

Can we continue to neglect genomic variation in introgression rates when inferring the history of speciation? A case study in a Mytilus hybrid zone.

The use of molecular data to reconstruct the history of divergence and gene flow between populations of closely related taxa represents a challenging problem. It has been proposed that the long-standing debate about the geography of speciation can be resolved by comparing the likelihoods of a model of isolation with migration and a model of secondary contact. However, data are commonly only fit to a model of isolation with migration and rarely tested against the secondary contact alternative. Furthermore, most demographic inference methods have neglected variation in introgression rates and assume that the gene flow parameter (Nm) is similar among loci. Here, we show that neglecting this source of variation can give misleading results. We analysed DNA sequences sampled from populations of the marine mussels, Mytilus edulis and M. galloprovincialis, across a well-studied mosaic hybrid zone in Europe and evaluated various scenarios of speciation, with or without variation in introgression rates, using an Approximate Bayesian Computation (ABC) approach. Models with heterogeneous gene flow across loci always outperformed models assuming equal migration rates irrespective of the history of gene flow being considered. By incorporating this heterogeneity, the best-supported scenario was a long period of allopatric isolation during the first three-quarters of the time since divergence followed by secondary contact and introgression during the last quarter. By contrast, constraining migration to be homogeneous failed to discriminate among any of the different models of gene flow tested. Our simulations thus provide statistical support for the secondary contact scenario in the European Mytilus hybrid zone that the standard coalescent approach failed to confirm. Our results demonstrate that genomic variation in introgression rates can have profound impacts on the biological conclusions drawn from inference methods and needs to be incorporated in future studies.

SlimCodeML: An Optimized Version of CodeML for the Branch-Site Model

CodeML (part of the PAML package) im- plements a maximum likelihood-based approach to de- tect positive selection on a specific branch of a given phylogenetic tree. While CodeML is widely used, it is very compute-intensive. We present SlimCodeML, an optimized version of CodeML for the branch-site model. Our performance analysis shows that SlimCodeML substantially outperforms CodeML (up to 9.38 times faster), especially for large-scale genomic analyses.

Do habitat suitability models reliably predict the recovery areas of threatened species?

1. Identifying those areas suitable for recolonization by threatened species is essential to support efficient conservation policies. Habitat suitability models (HSM) predict species' potential distributions, but the quality of their predictions should be carefully assessed when the species-environment equilibrium assumption is violated.2. We studied the Eurasian otter Lutra lutra, whose numbers are recovering in southern Italy. To produce widely applicable results, we chose standard HSM procedures and looked for the models' capacities in predicting the suitability of a recolonization area. We used two fieldwork datasets: presence-only data, used in the Ecological Niche Factor Analyses (ENFA), and presence-absence data, used in a Generalized Linear Model (GLM). In addition to cross-validation, we independently evaluated the models with data from a recolonization event, providing presences on a previously unoccupied river.3. Three of the models successfully predicted the suitability of the recolonization area, but the GLM built with data before the recolonization disagreed with these predictions, missing the recolonized river's suitability and badly describing the otter's niche. Our results highlighted three points of relevance to modelling practices: (1) absences may prevent the models from correctly identifying areas suitable for a species spread; (2) the selection of variables may lead to randomness in the predictions; and (3) the Area Under Curve (AUC), a commonly used validation index, was not well suited to the evaluation of model quality, whereas the Boyce Index (CBI), based on presence data only, better highlighted the models' fit to the recolonization observations.4. For species with unstable spatial distributions, presence-only models may work better than presence-absence methods in making reliable predictions of suitable areas for expansion. An iterative modelling process, using new occurrences from each step of the species spread, may also help in progressively reducing errors.5. Synthesis and applications. Conservation plans depend on reliable models of the species' suitable habitats. In non-equilibrium situations, such as the case for threatened or invasive species, models could be affected negatively by the inclusion of absence data when predicting the areas of potential expansion. Presence-only methods will here provide a better basis for productive conservation management practices.

Models that include supercoiling of topological domains reproduce several known features of interphase chromosomes.

Understanding the structure of interphase chromosomes is essential to elucidate regulatory mechanisms of gene expression. During recent years, high-throughput DNA sequencing expanded the power of chromosome conformation capture (3C) methods that provide information about reciprocal spatial proximity of chromosomal loci. Since 2012, it is known that entire chromatin in interphase chromosomes is organized into regions with strongly increased frequency of internal contacts. These regions, with the average size of ∼1 Mb, were named topological domains. More recent studies demonstrated presence of unconstrained supercoiling in interphase chromosomes. Using Brownian dynamics simulations, we show here that by including supercoiling into models of topological domains one can reproduce and thus provide possible explanations of several experimentally observed characteristics of interphase chromosomes, such as their complex contact maps.

Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.

Integrating species distribution models (SDMs) and phylogeography for two species of Alpine Primula.

The major intention of the present study was to investigate whether an approach combining the use of niche-based palaeodistribution modeling and phylo-geography would support or modify hypotheses about the Quaternary distributional history derived from phylogeographic methods alone. Our study system comprised two closely related species of Alpine Primula. We used species distribution models based on the extant distribution of the species and last glacial maximum (LGM) climate models to predict the distribution of the two species during the LGM. Phylogeographic data were generated using amplified fragment length polymorphisms (AFLPs). In Primula hirsuta, models of past distribution and phylogeographic data are partly congruent and support the hypothesis of widespread nunatak survival in the Central Alps. Species distribution models (SDMs) allowed us to differentiate between alpine regions that harbor potential nunatak areas and regions that have been colonized from other areas. SDMs revealed that diversity is a good indicator for nunataks, while rarity is a good indicator for peripheral relict populations that were not source for the recolonization of the inner Alps. In P. daonensis, palaeo-distribution models and phylogeographic data are incongruent. Besides the uncertainty inherent to this type of modeling approach (e.g., relatively coarse 1-km grain size), disagreement of models and data may partly be caused by shifts of ecological niche in both species. Nevertheless, we demonstrate that the combination of palaeo-distribution modeling with phylogeographical approaches provides a more differentiated picture of the distributional history of species and partly supports (P. hirsuta) and partly modifies (P. daonensis and P. hirsuta) hypotheses of Quaternary distributional history. Some of the refugial area indicated by palaeodistribution models could not have been identified with phylogeographic data.

A reassessment of models for hydrocarbon generation in the Khibiny nepheline syenite complex, Kola Peninsula, Russia

Although hydrocarbon-bearing fluids have been known from the alkaline igneous rocks of the Khibiny intrusion for many years, their origin remains enigmatic. A recently proposed model of post-magmatic hydrocarbon (HC) generation through Fischer-Tropsch (FT) type reactions suggests the hydration of Fe-bearing phases and release of H-2 which reacts with magmatically derived CO2 to form CH4 and higher HCs. However, new petrographic, microthermometric, laser Raman, bulk gas and isotope data are presented and discussed in the context of previously published work in order to reassess models of HC generation. The gas phase is dominated by CH4 with only minor proportions of higher hydrocarbons. No remnants of the proposed primary CO2-rich fluid are found in the complex. The majority of the fluid inclusions are of secondary nature and trapped in healed microfractures. This indicates a high fluid flux after magma crystallisation. Entrapment conditions for fluid inclusions are 450-550 degrees C at 2.8-4.5 kbar. These temperatures are too high for hydrocarbon gas generation through the FT reaction. Chemical analyses of rims of Fe-rich phases suggest that they are not the result of alteration but instead represent changes in magma composition during crystallisation. Furthermore, there is no clear relationship between the presence of Fe-rich minerals and the abundance of fluid inclusion planes (FIPs) as reported elsewhere. delta C-13 values for methane range from -22.4% to -5.4%, confirming a largely abiogenic origin for the gas. The presence of primary CH4-dominated fluid inclusions and melt inclusions, which contain a methane-rich gas phase, indicates a magmatic origin of the HCs. An increase in methane content, together with a decrease in delta C-13 isotope values towards the intrusion margin suggests that magmatically derived abiogenic hydrocarbons may have mixed with biogenic hydrocarbons derived from the surrounding country rocks. (C) 2006 Elsevier BV. All rights reserved.

Falsification and corroboration of conceptual hydrological models using geophysical data

Geophysical data may provide crucial information about hydrological properties, states, and processes that are difficult to obtain by other means. Large data sets can be acquired over widely different scales in a minimally invasive manner and at comparatively low costs, but their effective use in hydrology makes it necessary to understand the fidelity of geophysical models, the assumptions made in their construction, and the links between geophysical and hydrological properties. Geophysics has been applied for groundwater prospecting for almost a century, but it is only in the last 20 years that it is regularly used together with classical hydrological data to build predictive hydrological models. A largely unexplored venue for future work is to use geophysical data to falsify or rank competing conceptual hydrological models. A promising cornerstone for such a model selection strategy is the Bayes factor, but it can only be calculated reliably when considering the main sources of uncertainty throughout the hydrogeophysical parameter estimation process. Most classical geophysical imaging tools tend to favor models with smoothly varying property fields that are at odds with most conceptual hydrological models of interest. It is thus necessary to account for this bias or use alternative approaches in which proposed conceptual models are honored at all steps in the model building process.

Impact of model complexity on cross-temporal transferability in Maxent species distribution models: An assessment using paleobotanical data

Maximum entropy modeling (Maxent) is a widely used algorithm for predicting species distributions across space and time. Properly assessing the uncertainty in such predictions is non-trivial and requires validation with independent datasets. Notably, model complexity (number of model parameters) remains a major concern in relation to overfitting and, hence, transferability of Maxent models. An emerging approach is to validate the cross-temporal transferability of model predictions using paleoecological data. In this study, we assess the effect of model complexity on the performance of Maxent projections across time using two European plant species (Alnus giutinosa (L.) Gaertn. and Corylus avellana L) with an extensive late Quaternary fossil record in Spain as a study case. We fit 110 models with different levels of complexity under present time and tested model performance using AUC (area under the receiver operating characteristic curve) and AlCc (corrected Akaike Information Criterion) through the standard procedure of randomly partitioning current occurrence data. We then compared these results to an independent validation by projecting the models to mid-Holocene (6000 years before present) climatic conditions in Spain to assess their ability to predict fossil pollen presence-absence and abundance. We find that calibrating Maxent models with default settings result in the generation of overly complex models. While model performance increased with model complexity when predicting current distributions, it was higher with intermediate complexity when predicting mid-Holocene distributions. Hence, models of intermediate complexity resulted in the best trade-off to predict species distributions across time. Reliable temporal model transferability is especially relevant for forecasting species distributions under future climate change. Consequently, species-specific model tuning should be used to find the best modeling settings to control for complexity, notably with paleoecological data to independently validate model projections. For cross-temporal projections of species distributions for which paleoecological data is not available, models of intermediate complexity should be selected.