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In this doctoral thesis, I present my research within the field of Mathematical Finance, focused on topics arising within the financial ‘xVA’ framework, in which classical asset pricing theory is augmented to accommodate additional frictions and risks inherent in modern risk management. The first two main chapters of our work revolve around the collateral choice option, a financial option that emerges when there is the possibility to select the collateral between various currencies or assets. We phrase this problem in terms of underlying collateral spreads, for which we develop a stochastic model leading to the representation of the option price as a non-linear functional of a stochastic process which is obtained by taking the maximum of the stochastic processes used to depict the collateral spreads. The lack of tractability of this model is resolved by imposing a specific ‘common factor’ structure onto the marginal distributions of the collateral spreads, from which we obtain an estimator for the option value. This is further refined through enhancements to account for the dynamics of the process. We analyse the numerical complexity of the obtained approximators and their behaviour within the parameter space. We further apply this model towards sensitivity calculations of an asset imbued with the collateral choice option. We further consider the hedging problem posed by such an asset and develop a variance-minimising hedging strategy based on the assumption of stochastic collateral spreads.In the third main chapter, we consider the efficient calculation of expected exposure sensitivities. The objective here is to improve the numerical complexity of Monte Carlo simulations involving many portfolio valuations. We replace costly exact valuation functions with an interpolation scheme, in which the interpolation points are determined by the probability distribution of the random variables underlying the assets in the portfolio. We utilise this approach to efficiently co, Dans cette thèse de doctorat, je présente mes recherches dans le domaine de la Finance Mathématique, centrées sur des sujets émergeant dans le cadre financier du « xVA », où la théorie classique de tarification des actifs est augmentée pour accommoder des frictions et des risques supplémentaires inhérents à la gestion moderne des risques. Les deux premiers chapitres principaux de notre travail tournent autour de l'option de choix de collatéral, une option financière qui émerge lorsqu'il y a la possibilité de sélectionner le collatéral entre différentes devises ou actifs. Nous formulons ce problème en termes de spreads de collatéral sous-jacents, pour lesquels nous développons un modèle stochastique menant à la représentation du prix de l'option comme une fonctionnelle non linéaire d'un processus stochastique qui est obtenu en prenant le maximum des processus stochastiques utilisés pour modéliser les spreads de collatéral. L'absence de solution explicite de ce modèle est résolue en imposant une structure de « facteur commun » spécifique sur les distributions marginales des spreads de collatéral, à partir de laquelle nous obtenons un estimateur pour la valeur de l'option. Ceci est encore affiné par des améliorations pour tenir compte de la dynamique du processus. Nous analysons la complexité numérique des approximations obtenues et leur comportement dans l'espace paramétrique. Nous appliquons en outre ce modèle aux calculs de sensibilité d'un actif doté de l'option de choix de collatéral. Nous considérons également le problème de couverture posé par un tel actif et développons une stratégie de couverture minimisant la variance basée sur l'hypothèse de spreads de collatéral stochastiques.Dans le troisième chapitre principal, nous considérons le calcul efficace des sensibilités de l’ « expected exposure ». L'objectif ici est d'améliorer la complexité numérique des simulations de Monte Carlo impliquant de nombreuses évaluations de portefeuille. Nous remplaçons les foncti, Doctorat en Sciences, info:eu-repo/semantics/nonPublished

Dominance relations and diagnostic tools based on Lorenz and Concentration curves in order to compare competing estimators of the regression function have recently been proposed. This approach turns out to be equivalent to forecast dominance when the estimators under consideration are auto-calibrated. A new characterization of auto-calibration is established, based on the graphs of Lorenz and Concentration curves. This result is exploited to propose an effective testing procedure for auto-calibration. A simulation study is conducted to evaluate its performances and its relevance for practice is demonstrated on an insurance data set., SCOPUS: ar.j, info:eu-repo/semantics/published

Green infrastructure (GI) is increasingly linked to urban water management and can contribute to achieving water security in communities. This research uses a variation-finding comparative approach to recognize how far GI solutions are currently used to address water security in the urban developments of Monterrey City, Mexico, and Brussels-Capital Region, Belgium. A comparative content analysis of seven related urban development/sectoral plans is conducted using ATLAS.ti 9 software. The results depict the overall distribution of GI implementations, their typologies and spatial scales, water-security aspects that are addressed by GI, and the related definitions in the plans. In general, our analysis does not present a promising situation for the Monterrey case, although it reveals that policymakers have started to use GI in urban plans to address water security. Considering Brussels’ conditions, although GI solutions are much more frequent and advanced than in Monterrey plans, the region cannot be considered a frontrunner of GI policies. Comparing these two remarkably diverse areas is beneficial to illuminate universal aspects of planning, as the method provides an opportunity to gain insight from a multi-city perspective, whether developed or developing, showing the potential areas to advance urban policies., SCOPUS: re.j, info:eu-repo/semantics/published

We consider the propagation of a stochastic SIR-type epidemic in two connected populations: a relatively small local population of interest which is surrounded by a much larger external population. External infectives can temporarily enter the small population and contribute to the spread of the infection inside this population. The rules for entry of infectives into the small population as well as their length of stay are modeled by a general Markov queueing system. Our main objective is to determine the distribution of the total number of infections within both populations. To do this, the approach we propose consists of deriving a family of martingales for the joint epidemic processes and applying classical stopping time or convergence theorems. The study then focuses on several particular cases where the external infection is described by a linear branching process and the entry of external infectives obeys certain specific rules. Some of the results obtained are illustrated by numerical examples., SCOPUS: ar.j, info:eu-repo/semantics/published

Summary: SIMSApiper is a Nextflow pipeline that creates reliable, structure-informed MSAs of thousands of protein sequences faster than standard structure-based alignment methods. Structural information can be provided by the user or collected by the pipeline from online resources. Parallelization with sequence identity-based subsets can be activated to significantly speed up the alignment process. Finally, the number of gaps in the final alignment can be reduced by leveraging the position of conserved secondary structure elements., SCOPUS: ar.j, info:eu-repo/semantics/published

Motivation: Whole exome sequencing (WES) has emerged as a powerful tool for genetic research, enabling the collection of a tremendous amount of data about human genetic variation. However, properly identifying which variants are causative of a genetic disease remains an important challenge, often due to the number of variants that need to be screened. Expanding the screening to combinations of variants in two or more genes, as would be required under the oligogenic inheritance model, simply blows this problem out of proportion. Results: We present here the High-throughput oligogenic prioritizer (Hop), a novel prioritization method that uses direct oligogenic information at the variant, gene and gene pair level to detect digenic variant combinations in WES data. This method leverages information from a knowledge graph, together with specialized pathogenicity predictions in order to effectively rank variant combinations based on how likely they are to explain the patient’s phenotype. The performance of Hop is evaluated in cross-validation on 36 120 synthetic exomes for training and 14 280 additional synthetic exomes for independent testing. Whereas the known pathogenic variant combinations are found in the top 20 in approximately 60% of the cross-validation exomes, 71% are found in the same ranking range when considering the independent set. These results provide a significant improvement over alternative approaches that depend simply on a monogenic assessment of pathogenicity, including early attempts for digenic ranking using monogenic pathogenicity scores., SCOPUS: ar.j, info:eu-repo/semantics/published

Stein's method is used to study discrete representations of multidimensional distributions that arise as approximations of states of quantum harmonic oscillators. These representations model how quantum effects result from the interaction of finitely many classical 'worlds', with the role of sample size played by the number of worlds. Each approximation arises as the ground state of a Hamiltonian involving a particular interworld potential function. Our approach, framed in terms of spherical coordinates, provides the rate of convergence of the discrete approximation to the ground state in terms of Wasserstein distance. Applying a novel Stein's method technique to the radial component of the ground state solution, the fastest rate of convergence to the ground state is found to occur in three dimensions., SCOPUS: ar.j, info:eu-repo/semantics/published

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Stein’s method compares probability distributions through the study of a class of linear operators called Stein operators.While mainly studied in probability and used to underpin theoretical statistics, Stein’s method has led to significant advances in computational statistics in recent years. The goal of this survey is to bring together some of these recent developments, and in doing so, to stimulate further research into the successful field of Stein’s method and statistics. The topics we discuss include tools to benchmark and compare sampling methods such as approximate Markov chain Monte Carlo, deterministic alternatives to sampling methods, control variate techniques, parameter estimation and goodness-of-fit testing, SCOPUS: ar.j, info:eu-repo/semantics/published

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Power laws and power laws with exponential cut-off are two distinct families of distributions on the positive real half-line. In the present paper, we propose a unified treatment of both families by building a family of distributions that interpolates between them, which we call Interpolating Family (IF) of distributions. Our original construction, which relies on techniques from statistical physics, provides a connection for hitherto unrelated distributions like the Pareto and Weibull distributions, and sheds new light on them. The IF also contains several distributions that are neither of power law nor of power law with exponential cut-off type. We calculate quantile-based properties, moments and modes for the IF. This allows us to review known properties of famous distributions on (Formula presented.) and to provide in a single sweep these characteristics for various less known (and new) special cases of our Interpolating Family., SCOPUS: ar.j, info:eu-repo/semantics/published

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Contaminated water and poor sanitation are associated with disease transmission. Absent, inadequate, or improperly managed water resources and sanitation systems expose individuals to preventable health risks. Billions of people lack access to these basic services today and will remain in this condition for decades to come. As we are usually thinking and talking about water, sanitation and hygiene services have changed. Looking back at the history of water, sanitation, and hygiene can help us understand the challenges and opportunities of these issues and draw lessons to achieve sustainable development in the future. Throughout history, civilizations have successfully experimented with treating water and using it for drinking, sanitation, and agriculture. For example, the Minoan civilizations originally focused on water treatment and cleaning to improve the aesthetic properties of drinking water. During prehistoric times, Minoan and Indus Valley civilizations, dating back to about 2000 BC, were the first to focus on the treatment of water supplies. From the early Minoan period, they relied on rainwater collection. During historic times, Hippocrates was the first to invent and used a water filter in the form of a cloth bag, at about 400 BC, known today as the Hippocrates Sleeve. The Romans perfected existing water technologies on a larger scale and initiated their spread throughout the Empire. Hygiene in ancient Rome was promoted by the famous public baths and toilets, which were supplied with water through widely branched aqueducts that had a high standard of cleanliness for the time and were regularly maintained., SCOPUS: re.j, info:eu-repo/semantics/published

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Extending rank-based inference to a multivariate setting such as multiple-output regression or MANOVA with unspecified d-dimensional error density has remained an open problem for more than half a century. None of the many solutions proposed so far is enjoying the combination of distribution-freeness and efficiency that makes rank-based inference a successful tool in the univariate setting. A concept of center-outward multivariate ranks and signs based on measure transportation ideas has been introduced recently. Center-outward ranks and signs are not only distribution-free but achieve in dimension d > 1 the (essential) maximal ancillarity property of traditional univariate ranks. In the present case, we show that fully distribution-free testing procedures based on center-outward ranks can achieve parametric efficiency. We establish the Hájek representation and asymptotic normality results required in the construction of such tests in multiple-output regression and MANOVA models. Simulations and an empirical study demonstrate the excellent performance of the proposed procedures., SCOPUS: ar.j, info:eu-repo/semantics/published

Many marine and terrestrial species live in groups, whose sizes and dynamics can vary depending on the type and strength of their social interactions. Typical examples of such groups in vertebrates are schools of fish or flocks of bird. Natural habitats can encompass a wide range of spatial heterogeneities, which can also shape the structure of animal groups, depending on the interplay between the attraction/repulsion of environmental cues and social interactions. A key issue in modern applied ecology and conservation is the need to understand the relationship between these ethological and ecological scales in order to account for the social behaviour of animals in their natural environments. Here, we introduce a modeling approach which studies animal groups within heterogeneous habitats constituted by a set of aggregative sites. The model properties are investigated considering the case study of tropical tuna schools and their associative behavior with floating objects, a question of global concern, given the thousands of floating objects deployed by industrial tropical tuna fisheries worldwide. The effects of increasing numbers of aggregative sites (floating objects) on tuna schools are studied. This study offers a general modeling framework to study social species in their habitats, accounting for both ethological and ecological drivers of animal group dynamics., SCOPUS: ar.j, info:eu-repo/semantics/published

We use a minimalistic mathematical model with a limited number of parameters to evaluate the impact of interindividual differences in the collective decision-making of a group. As it turns out, in most cases, heterogeneous groups are more efficient in their decision-making than homogenous ones, especially when considering small group sizes. In reality, being different disfavours the emergence of an hysteresis and a collective threshold which are characteristics of such cooperative species while keeping inter-attractions the same between individuals. Finally, when the cooperativity becomes very large, we observe an explosion of accessible stable states., SCOPUS: ar.j, info:eu-repo/semantics/published

Consider a linear elliptic partial differential equation in divergence form with a random coefficient field. The solution-operator displays fluctuations around its expectation. The recently-developed pathwise theory of fluctuations in stochastic homogenization reduces the characterization of these fluctuations to those of the so-called standard homogenization commutator. In this contribution, we investigate the scaling limit of this key quantity: starting from a Gaussian-like coefficient field with possibly strong correlations, we establish the convergence of the rescaled commutator to a fractional Gaussian field, depending on the decay of correlations of the coefficient field, and we investigate the (non)degeneracy of the limit. This extends to general dimension d ≥ 1 previous results so far limited to dimension d = 1, and to the continuum setting with strong correlations recent results in the discrete i.i.d. case., SCOPUS: ar.j, info:eu-repo/semantics/published

This work is concerned with the mathematical analysis of the bulk rheology of random suspensions of rigid particles settling under gravity in viscous fluids. Each particle generates a fluid flow that in turn acts on other particles and hinders their settling. In an equilibrium perspective, for a given ensemble of particle positions, we analyze both the associated mean settling speed and the velocity fluctuations of individual particles. In the 1970s, Batchelor gave a proper definition of the mean settling speed, a 60-year-old open problem in physics, based on the appropriate renormalization of long-range particle contributions. In the 1980s, a celebrated formal calculation by Caflisch and Luke suggested that velocity fluctuations in dimension d= 3 should diverge with the size of the sedimentation tank, contradicting both intuition and experimental observations. The role of long-range self-organization of suspended particles in form of hyperuniformity was later put forward to explain additional screening of this divergence in steady-state observations. In the present contribution, we develop the first rigorous theory that allows to justify all these formal calculations of the physics literature., SCOPUS: ar.j, info:eu-repo/semantics/published

This work is devoted to the asymptotic behavior of eigenvalues of an elliptic operator with rapidly oscillating random coefficients on a bounded domain with Dirichlet boundary conditions. A sharp convergence rate is obtained for eigenvalues towards those of the homogenized problem, as well as a quantitative two-scale expansion result for eigenfunctions. Next, a quantitative central limit theorem is established for fluctuations of isolated eigenvalues; more precisely, a pathwise characterization of eigenvalue fluctuations is obtained in terms of the so-called homogenization commutator, in parallel with the recent fluctuation theory for the solution operator., SCOPUS: ar.j, info:eu-repo/semantics/published

Thanks to its outstanding performances, boosting has rapidly gained wide acceptance among actuaries. To speed up calculations, boosting is often applied to gradients of the loss function, not to responses (hence the name gradient boosting). When the model is trained by minimizing Poisson deviance, this amounts to apply the least-squares principle to raw residuals. This exposes gradient boosting to the same problems that lead to replace least-squares with Poisson Generalized Linear Models (GLM) to analyze low counts (typically, the number of reported claims at policy level in personal lines). This paper shows that boosting can be conducted directly on the response under Tweedie loss function and log-link, by adapting the weights at each step. Numerical illustrations demonstrate similar or better performances compared to gradient boosting when trees are used as weak learners, with a higher level of transparency since responses are used instead of gradients., SCOPUS: ar.j, info:eu-repo/semantics/published

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In the present paper, we show that several classical nonparametric tests for multivariate location in the Euclidean case can be adapted to nonparametric tests for the location problem on hyperspheres. The tests we consider are spatial signed-rank tests for location on hyperspheres. We compute the asymptotic powers of the latter tests in the classical rotationally symmetric case. In particular, we show that the spatial signed-rank test uniformly dominates the spatial sign test and has performances that are extremely close to the asymptotically optimal test in the well-known von Mises–Fisher case. Monte-Carlo simulations confirm our asymptotic results., SCOPUS: ar.j, info:eu-repo/semantics/published

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In this note, we derive upper bounds on Kendall’s tau and Spearman’s rho for multivariate zero-inflated continuous variables often encountered in insurance. A lower bound for Spearman’s rho is also established in the bivariate case. These bounds are easy to compute and can be estimated from a data set of zero-inflated random vectors as illustrated in this note with a motor insurance portfolio., SCOPUS: ar.j, info:eu-repo/semantics/published