On multivariate extensions of Conditional-Tail-Expectation

Cousin, Areski; Bernardino, Éléna Di

doi:10.1016/j.insmatheco.2014.01.013

Cited by 31 publications

(31 citation statements)

References 33 publications

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“…Then, they explored the function properties and relation equations. Cousin and Bernardino (2014) extended the above studies to the CTE. proposed the multivariate quantile vector for multi-dimensional data.…”

Section: Introductionmentioning

confidence: 94%

Multivariate CTE for copula distributions

Hong¹,

Kim²

2017

Journal of the Korean Data and Information Science Society

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The CTE (conditional tail expectation) is a useful risk management measure for a diversified investment portfolio that can be generally estimated by using a transformed univariate distribution. proposed a multivariate CTE based on multivariate quantile vectors, and explored its characteristics for multivariate normal distributions. Since most real financial data is not distributed symmetrically, it is problematic to apply the CTE to normal distributions. In order to obtain a multivariate CTE for various kinds of joint distributions, distribution fitting methods using copula functions are proposed in this work. Among the many copula functions, the Clayton, Frank, and Gumbel functions are considered, and the multivariate CTEs are obtained by using their generator functions and parameters. These CTEs are compared with CTEs obtained using other distribution functions. The characteristics of the multivariate CTEs are discussed, as are the properties of the distribution functions and their corresponding accuracy. Finally, conclusions are derived and presented with illustrative examples.

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Section: Introductionmentioning

confidence: 94%

Multivariate CTE for copula distributions

Hong¹,

Kim²

2017

Journal of the Korean Data and Information Science Society

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“…It is closely related to the notion of quantile which has therefore been extensively studied in dimension one. For a random variable X that represents the In the following we deal with the multivariate version of Conditional-Tail-Expectation, proposed by Di Bernardino et al (2011), Cousin and Di Bernardino (2012). It is constructed as the conditional expectation of a multivariate random vector given that the latter is located in a particular set corresponding to the α-upper level set of the associated multivariate distribution function (in a bivariate setting see Di Bernardino et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

“…Some commonly used multivariate CTE measures are: Cai and Li, 2005). Furthermore, for a comparison between measures in (2)-(4) and (1) we refer to Cousin and Di Bernardino (2012). In the recent literature, some efforts have been done to provide a consistent estimation of measures in (2)-(4).…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we propose a new estimator for the multivariate risk measure defined by (1) above, and introduced by Di Bernardino et al (2011), Cousin and Di Bernardino (2012).…”

Section: Introductionmentioning

confidence: 99%

“…

AbstractThis paper deals with the problem of estimating the Multivariate version of the Conditional-TailExpectation, proposed by Cousin and Di Bernardino (2012). We propose a new non-parametric estimator for this multivariate risk-measure, which is essentially based on the Kendall's process (see Genest and Rivest, 1993).

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Estimation of multivariate conditional-tail-expectation using Kendall's process

Bernardino

Prieur

2014

Journal of Nonparametric Statistics

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This paper deals with the problem of estimating the Multivariate version of the Conditional-TailExpectation, proposed by Cousin and Di Bernardino (2012). We propose a new non-parametric estimator for this multivariate risk-measure, which is essentially based on the Kendall's process (see Genest and Rivest, 1993). Using the Central Limit Theorem for the Kendall's process, proved by Barbe et al. (1996), we provide a functional Central Limit Theorem for our estimator. We illustrate the practical properties of our estimator on simulations. A real case in environmental framework is also analyzed. The performances of our new estimator are compared to the ones of the level sets-based estimator, previously proposed in Di Bernardino et al. (2011).

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A multivariate copula‐based framework for dealing with hazard scenarios and failure probabilities

Salvadori

Durante

Michele

et al. 2016

Water Resources Research

204

173

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This paper is of methodological nature, and deals with the foundations of Risk Assessment.\ud Several international guidelines have recently recommended to select appropriate/relevant Hazard Scenarios\ud in order to tame the consequences of (extreme) natural phenomena. In particular, the scenarios should\ud be multivariate, i.e., they should take into account the fact that several variables, generally not independent,\ud may be of interest. In this work, it is shown how a Hazard Scenario can be identified in terms of (i) a specific\ud geometry and (ii) a suitable probability level. Several scenarios, as well as a Structural approach, are presented,\ud and due comparisons are carried out. In addition, it is shown how the Hazard Scenario approach\ud illustrated here is well suited to cope with the notion of Failure Probability, a tool traditionally used for\ud design and risk assessment in engineering practice. All the results outlined throughout the work are based\ud on the Copula Theory, which turns out to be a fundamental theoretical apparatus for doing multivariate risk\ud assessment: formulas for the calculation of the probability of Hazard Scenarios in the general multidimensional\ud case (d 2) are derived, and worthy analytical relationships among the probabilities of occurrence of\ud Hazard Scenarios are presented. In addition, the Extreme Value and Archimedean special cases are dealt\ud with, relationships between dependence ordering and scenario levels are studied, and a counter-example\ud concerning Tail Dependence is shown. Suitable indications for the practical application of the techniques\ud outlined in the work are given, and two case studies illustrate the procedures discussed in the pape

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On multivariate extensions of Conditional-Tail-Expectation

Cited by 31 publications

References 33 publications

Multivariate CTE for copula distributions

Multivariate CTE for copula distributions

Estimation of multivariate conditional-tail-expectation using Kendall's process

A multivariate copula‐based framework for dealing with hazard scenarios and failure probabilities

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