Sklar's theorem in an imprecise setting

Sklar's theorem is an important tool that connects bidimensional distribution functions with their marginals by means of a copula. When there is imprecision about the marginals, we can model the available information by means of p-boxes, that are pairs of ordered distribution functions. Similarly, we can consider a set of copulas instead of a single one. We study the extension of Sklar's theorem under these conditions, and link the obtained results to stochastic ordering with imprecision

Final solution to the problem of relating a true copula to an imprecise copula

In this paper we solve in the negative the problem proposed in this journal (I. Montes et al., Sklar's theorem in an imprecise setting, Fuzzy Sets and Systems, 278 (2015), 48-66) whether an order interval defined by an imprecise copula contains a copula. Namely, if $\mathcal{C}$ is a nonempty set of copulas, then $\underline{C} = \inf\{C\}_{C\in\mathcal{C}}$ and $\overline{C}= \sup\{C\}_{C\in\mathcal{C}}$ are quasi-copulas and the pair $(\underline{C},\overline{C})$ is an imprecise copula according to the definition introduced in the cited paper, following the ideas of $p$-boxes. We show that there is an imprecise copula $(A,B)$ in this sense such that there is no copula $C$ whatsoever satisfying $A \leqslant C\leqslant B$. So, it is questionable whether the proposed definition of the imprecise copula is in accordance with the intentions of the initiators. Our methods may be of independent interest: We upgrade the ideas of Dibala et al. (Defects and transformations of quasi-copulas, Kybernetika, 52 (2016), 848-865) where possibly negative volumes of quasi-copulas as defects from being copulas were studied.Comment: 20 pages; added Conclusion, added some clarifications in proofs, added some explanations at the beginning of each section, corrected typos, results remain the sam

Constructing copulas from shock models with imprecise distributions

The omnipotence of copulas when modeling dependence given marg\-inal distributions in a multivariate stochastic situation is assured by the Sklar's theorem. Montes et al.\ (2015) suggest the notion of what they call an \emph{imprecise copula} that brings some of its power in bivariate case to the imprecise setting. When there is imprecision about the marginals, one can model the available information by means of $p$-boxes, that are pairs of ordered distribution functions. By analogy they introduce pairs of bivariate functions satisfying certain conditions. In this paper we introduce the imprecise versions of some classes of copulas emerging from shock models that are important in applications. The so obtained pairs of functions are not only imprecise copulas but satisfy an even stronger condition. The fact that this condition really is stronger is shown in Omladi\v{c} and Stopar (2019) thus raising the importance of our results. The main technical difficulty in developing our imprecise copulas lies in introducing an appropriate stochastic order on these bivariate objects

A full scale Sklar's theorem in the imprecise setting

In this paper we present a surprisingly general extension of the main result of a paper that appeared in this journal: I. Montes et al., Sklar's theorem in an imprecise setting, Fuzzy Sets and Systems, 278 (2015), 48--66. The main tools we develop in order to do so are: (1) a theory on quasi-distributions based on an idea presented in a paper by R. Nelsen with collaborators; (2) starting from what is called (bivariate) $p$-box in the above mentioned paper we propose some new techniques based on what we call restricted (bivariate) $p$-box; and (3) a substantial extension of a theory on coherent imprecise copulas developed by M. Omladi\v{c} and N. Stopar in a previous paper in order to handle coherence of restricted (bivariate) $p$-boxes. A side result of ours of possibly even greater importance is the following: Every bivariate distribution whether obtained on a usual $\sigma$-additive probability space or on an additive space can be obtained as a copula of its margins meaning that its possible extraordinariness depends solely on its margins. This might indicate that copulas are a stronger probability concept than probability itself.Comment: 16 pages, minor change

A copula model for dependent competing risks

Many popular estimators for duration models require independent competing risks or independent censoring. In contrast, copula based estimators are also consistent in presence of dependent competing risks. In this paper we suggest a computationally convenient extension of the Copula Graphic Estimator (Zheng and Klein, 1995) to a model with more than two dependent competing risks. We analyse the applicability of this estimator by means of simulations and real world unemployment duration data from Germany. We obtain evidence that our estimator yields nice results if the dependence structure is known and that it is a powerful tool for the assessment of the relevance of (in-)dependence assumptions in applied duration research.Archimedean copula, dependent censoring, unemployment duration

A copula model for dependent competing risks

"Many popular estimators for duration models require independent competing risks or independent censoring. In contrast, copula based estimators are also consistent in presence of dependent competing risks. In this paper we suggest a computationally convenient extension of the Copula Graphic Estimator (Zheng and Klein, 1995) to a model with more than two dependent competing risks. We analyse the applicability of this estimator by means of simulations and real world unemployment duration data from Germany. We obtain evidence that our estimator yields nice results if the dependence structure is known and that it is a powerful tool for the assessment of the relevance of (in-)dependence assumptions in applied duration research." (Author's abstract, IAB-Doku) ((en)) Additional Information Appendix for the FDZ-Methodenreport No. 02/2009Risikoabschätzung - Modell, Wirkungsforschung - Methode, Methodologie, Arbeitsmarktpolitik - Erfolgskontrolle, ältere Arbeitnehmer, Leistungsanspruch - Dauer, Arbeitslosigkeitsdauer, IAB-Beschäftigtenstichprobe

Corporate Sustainable Development. Revisiting the Relationship between Corporate Social Responsibility Dimensions

With rising stakeholder concerns over sustainable development, corporate social responsibility (CSR) has become key for the business community, moving the business model beyond financial performance to a new voluntary paradigm based on natural resource conservation, social welfare, stakeholder engagement and economic performance. This article aims to answer whether profitable business is compatible with balanced sustainability by investigating the relationship between the economic, social, environmental and governance performance for a sample of global firms. A canonical vine (C‐vine) copula is used for this purpose. Results show the existence of a fairly strong positive relationship between economic, social and environmental performance. The corporate governance dimension is shown to have a weak relationship with the rest of the CSR dimensions. Important policy implications are derived from these results. Copyright © 2017 John Wiley & Sons, Ltd and ERP Environmentinfo:eu-repo/semantics/acceptedVersio

Sustainability and firm performance : evidence from corportate and farm level

This thesis approaches the question of sustainability and firm performance. In the contemporary business model, firm performance measurement must take into account not only economic profits, but also environmental and social issues, in order to ensure the sustainable development of the firm. By using advanced methodological approaches and exploring sustainability through a holistic view, this thesis contributes significantly to sustainability performance literature. Three specific objectives have been fulfilled through three papers that constitute the main body of the present thesis. The first article aims to answer whether profitable business is compatible with balanced sustainability by investigating the relationship between the economic, social, environmental and governance performance for a sample of global firms. A canonical vine (C-vine) copula is used for this purpose. Results show the existence of a fairly strong positive relationship between economic, social and environmental performance. The corporate governance dimension is shown to have a weak relationship with the rest of the corporate social responsibility (CSR) dimensions. Important policy implications are derived from these results. The second paper investigates the relationships among performance dimensions associated with corporate social responsibility focusing on the U.S. electric utility sector. Results of a statistical copula approach suggest that economic performance of utilities is compatible with environmental, social, and governance performance. The CSR model has the potential to help U.S. electric utilities become better corporate citizens while also obtaining higher economic profits. The third paper investigates farms’ stochastic production technology as the interaction of three-main types of sub-technologies that govern, respectively, the production of agricultural commodities, environmental pollution, and social outputs of agricultural activities. The model is empirically implemented through a Data Envelopment Analysis (DEA) model. The empirical application is based on a survey of Catalan arable crop farms. On average, we find our sample farms to display high technical and social performance, while they show relatively poor environmental performance.Esta tesis aborda la cuestión de la sostenibilidad y el rendimiento de la empresa. En el modelo de negocio contemporáneo, la medición del rendimiento de la empresa debe tener en cuenta no solo las ganancias económicas, sino también las cuestiones ambientales y sociales, para garantizar el desarrollo sostenible de la empresa. Mediante el uso de enfoques metodológicos avanzados y la exploración de la sostenibilidad a través de una visión holística, esta tesis contribuye significativamente a la literatura sobre la sostenibilidad. Tres objetivos específicos se han cumplido a través de tres documentos que constituyen el cuerpo principal de la presente tesis. El primer artículo tiene como objetivo responder si el negocio rentable es compatible con la sostenibilidad equilibrada, mediante la investigación de la relación entre el desempeño económico, social, medio-ambiental y de gobernanza de una muestra de empresas globales. Un modelo canónico de viña de copulas (C-vine) se usa para este propósito. Los resultados muestran la existencia de una relación positiva bastante fuerte entre el desempeño económico, social y ambiental. Se muestra que la dimensión de gobernanza corporativa tiene una relación débil con el resto de las dimensiones de la responsabilidad social corporativa (RSC). Importantes implicaciones de política se derivan de estos resultados. El segundo articulo investiga las relaciones entre las dimensiones de desempeño asociadas con la responsabilidad social corporativa que se centran en el sector de servicios eléctricos de los EE. UU. Los resultados obtenidos del análisis de las cópulas sugieren que el desempeño económico de las empresas eléctricas es compatible con el desempeño ambiental, social y de gobernanza. El modelo de la RSC tiene el potencial de ayudar a que los servicios eléctricos de los EE. UU. Se conviertan en mejores ciudadanos corporativos mientras se logran mayores beneficios económicos. El tercer trabajo investiga la tecnología de producción estocástica de las explotaciones agrícolas como una interacción de tres sub-tecnologías que gobiernan, respectivamente, la producción de productos agrícolas, la contaminación ambiental y los productos sociales de las actividades agrícolas. El modelo se implementa empíricamente a través de un modelo de Análisis Envolvente de Datos (DEA). La aplicación empírica se basa en una encuesta de explotaciones de cultivos en la región de Cataluña. En promedio, encontramos que nuestras explotaciones muestran un alto desempeño técnico y social, mientras que muestran un desempeño ambiental relativamente pobre

Capital requirements and claims recovery: A new perspective on solvency regulation

Protection of creditors is a key objective of financial regulation. Where the protection needs are high, that is, in banking and insurance, regulatory solvency requirements are an instrument to prevent that creditors incur losses on their claims. The current regulatory requirements based on value at risk (V@R) and average value at risk (AV@R) limit the probability of default of financial institutions, but they fail to control the size of recovery on creditors' claims in the case of default. We resolve this failure by developing a novel risk measure, recovery V@R. Our conceptual approach is flexible and allows the construction of general recovery risk measures for various risk management purposes. We provide detailed case studies and applications. We show that recovery risk measures can be used for performance-based management of business divisions of firms and discuss how to calibrate recovery risk measures to historical regulatory standards. Finally, we analyze how recovery risk measures react to the joint distributions of assets and liabilities on firms' balance sheets and compare the corresponding capital requirements with the current regulatory benchmarks based on V@R and AV@R