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Los órdenes estocásticos o las dominancias estocásticas tal como se conocen en Economía se han estudiado y aplicado ampliamente en diversidad de campos científicos, desde la Biología hasta la Ingeniería de Sistemas. Sin embargo, hasta donde llega nuestro conocimiento hay una laguna de aplicación dentro del ámbito de las Ciencias del Deporte. En este trabajo, pretendemos una primera aproximación a una posible aplicación de los órdenes estocásticos a un conjunto de datos de partidos de fútbol de LaLiga (España). Nuestro objetivo simplemente es mostrar como se puede ampliar una comparativa más allá de una simple comparación de métricas globales o totales. En particular, nos detendremos en los órdenes de dominancia estocástica de primer y segundo orden por ser los más intuitivos y de más sencilla interpretación y por ser los más usados en Economía., Stochastic orders or stochastic dominance as they are known in economics, have been widely studied and applied in a variety of scientific fields, from biology to Systems Engineering. However, to the best of our knowledge, there is an application gap in the field of Sports Analytics or Sports Sciences. In this paper, we attempt a first approach to a possible application of stochastic orders to a dataset of LaLiga (Spain) football matches. Our aim is simply to show how a comparison can be extended beyond a simple metric comparison. In particular, we will focus on the first and second dominance stochastic orders as they are the most intuitive and simple to interpret and are also the most widely used in economics.

The dissemination of research in cultural heritage preservation to the public is a task that needs new models and expressions, to capture the attention of the public and the assessment of results. With this purpose, a new educa‑ tional experience in Parque de las Ciencias (Science Park of Granada, Spain) was developed. The science window titled Hidden Face of Cultural Heritage (ScW‑CH) was an exhibition to show the risks (hazards + vulnerability) associ‑ ated to different artworks and materials of our cultural heritage (CH). ScW‑CH was led by the researchers themselves, in collaboration with museum specialists, in order to develop a new model that makes their research accessible to all demographics. An innovative methodology based into simulating a showcase, was designed to study hazards and vulnerability in CH. Therefore, the montage contained materials, equipment, information sheets, and guides to accompany visitors as storytellers. The aim of the exhibition, was for the visitors to understand the risks posed to our monuments and artworks from a scientific point of view, and to raise awareness about the care that we should give to our CH. The ScW‑CH was held for 6 months and visited by 8226 visitors. During the exhibition, a survey about the opinion of visitors was carried out to study the impact of the designed new model and assess the results of the expe‑ rience. The collected data was analysed by the Statistical Package for the Social Sciences (version 22.0). Visitors usually presented a medium–high initial interest about visiting this exhibition, and a medium–low level of knowledge of this subject. Thanks to ScW‑CH, 92% of visitors showed a very high learning level after the experience. The ratio of interest and learning in the ScW‑CH in relationship with the level of study showed that secondary school pupils had the high‑ est degree of interest and learning.

Como consecuencia de que los reguladores necesitan gestionar el riesgo en los distintos sectores, se está extendiendo de forma rápida una metodología basada en el riesgo. En las últimas décadas, este problema ha sido tratado en su mayoría en una versión univariante. Sin embargo, los riesgos envuelven normalmente varias variables aleatorias que son a menudo dependientes. Por tanto, es crucial trabajar en un marco multivariante. Por otro lado, los fenómenos están caracterizados frecuentemente por eventos extremos. Esta tesis trata fundamentalmente dos problemas: la definición de medidas de riesgo en un marco multivariante y la estimatión de medidas de riesgo multivariantes teniendo en cuenta eventos extremos. El Capítulo 1 es un capítulo introductorio. Presentamos el estado del arte para la noción de medidas de riesgo multivariantes. También, recordamos los principales resultados en Teoría de Cópulas, Teoría de Valores Extremos y Órdenes Estocásticos que son útiles en este trabajo . Se introducen dos nuevas medidas de riesgo multivariantes en el Capítulo 2. Varias propiedades interesantes y, caracterizaciones bajo condiciones de cópulas Arquimedianas, se estudian para las medidas de riesgo propuestas. Además, se obtienen estimadores semiparamétricos para las nuevas medidas, y son ejempli_cados considerando datos simulados y un conjunto de datos real de seguros. El Capítulo 3 se centra en la estimación extrema no paramétrica de las medidas multivariantes propuestas en el Capítulo 2. Para este propósito, primero analizamos el comportamiento en la cola de las distribuciones condicionadas que de_nen dichas medidas. El principal resultado está constituido por el Teorema Central del Límite de los estimadores extremos. El rendimiento de los estimadores extremos se evalúa en datos simulados y para un conjunto de datos real de precipitaciones. El estudio de la medida de riesgo multivariante asociada con the Component-wise Excess(C.-E.) design realization dada por Salvadori et, As a consequence of the need for regulators to manage risk in various sectors, a riskbased methodology is undergoing a fast expansion. Over recent decades, this problem has been mostly addressed via a univariate approach. However, risks usually involve several random variables that are often non-independent. Therefore, it is crucial to work in a multivariate setting. On the other hand, phenomena are frequently characterized by extreme events. This thesis is fundamentally concerned with two problems: the de_nition of risk measures in a multivariate setting, and the estimation of multivariate risk measures by taking extreme events into account. Chapter 1 is an introductory chapter. We present the state-of-art of the notion of multivariate risk measures. The main results in Copula Theory, Extreme Value Theory, and Stochastic Orders, which are useful in this work, are also provided. Two new multivariate risk measures are introduced in Chapter 2. Several interesting properties and, characterizations under Archimedean copulas, are studied for the proposed risk measures. Furthermore, semi-parametric estimators for the new measures are obtained and are then exempli_ed considering simulated data and a real insurance data-set. Chapter 3 deals with the non-parametric extreme estimation procedure of the multivariate measures proposed in Chapter 2. For this purpose, we _rst analyse the tail behaviour of the conditional distributions that de_ne the aforementioned measures. The main result is given by the Central limit Theorem of the extreme estimators. The performance of the extreme estimators is evaluated in simulated data and for a real rainfall data-set. The multivariate risk measure associated with the Component-wise Excess (C.-E.) design realization given by Salvadori et al. (2011) is outlined in Chapter 4. The explicit expression of the measure for Archimedean copulas is obtained. In addition, an extreme estimation procedure for the C.-E. design realization is provided and

CoVaR is a systemic risk measure proposed by Adrian and Brunnermeier (2011) able to measure a financial institution’s contribution to systemic risk and its contribution to the risk of other financial institutions. CoVaR stands for conditional Value-at-Risk, i.e. it indicates the Value at Risk for a financial institution that is conditional on a certain scenario. In this paper, two alternative extensions of the classic univariate Conditional Value-at-Risk are introduced in a multivariate setting. The two proposed multivariate CoVaRs are constructed from level sets of multivariate distribution functions (resp. of multivariate survival distribution functions). These vector-valued measures have the same dimension as the underlying risk portfolio. Several characterizations of these new risk measures are provided in terms of the copula structure and stochastic orderings of the marginal distributions. Interestingly, these results are consistent with existing properties on univariate risk measures. Furthermore, comparisons between existent risk measures and the proposed multivariate CoVaR are developed. Illustrations are given in the class of Archimedean copulas. Estimation procedure for the multivariate proposed CoVaRs is illustrated in simulated studies and insurance real data.