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1
Content available remote

Solution to an open problem about a transformation on the space of copulas

100%
Durante F., Fernández-Sánchez J., Trutschnig W.
Dependence Modeling
|
2014
|
tom 2
|
nr 1
EN
We solve a recent open problem about a new transformation mapping the set of copulas into itself. The obtained mapping is characterized in algebraic terms and some limit results are proved.
2
Content available remote

Generalized covariance inequalities

88%
Matuła P., Ziemba M.
Open Mathematics
|
2011
|
tom 9
|
nr 2
281-293
EN
We prove some inequalities for the difference between a joint distribution and the product of its marginals for arbitrary absolutely continuous random variables. Some applications of the obtained inequalities are also presented.
3
Content available remote

On the tail dependence in bivariate hydrological frequency analysis

88%
Lekina A., Chebana F., Ouarda T. B. M. J.
Dependence Modeling
|
2015
|
tom 3
|
nr 1
EN
In Bivariate Frequency Analysis (BFA) of hydrological events, the study and quantification of the dependence between several variables of interest is commonly carried out through Pearson’s correlation (r), Kendall’s tau (τ) or Spearman’s rho (ρ). These measures provide an overall evaluation of the dependence. However, in BFA, the focus is on the extreme events which occur on the tail of the distribution. Therefore, these measures are not appropriate to quantify the dependence in the tail distribution. To quantify such a risk, in Extreme Value Analysis (EVA), a number of concepts and methods are available but are not appropriately employed in hydrological BFA. In the present paper, we study the tail dependence measures with their nonparametric estimations. In order to cover a wide range of possible cases, an application dealing with bivariate flood characteristics (peak flow, flood volume and event duration) is carried out on three gauging sites in Canada. Results show that r, τ and ρ are inadequate to quantify the extreme risk and to reflect the dependence characteristics in the tail. In addition, the upper tail dependence measure, commonly employed in hydrology, is shown not to be always appropriate especially when considered alone: it can lead to an overestimation or underestimation of the risk. Therefore, for an effective risk assessment, it is recommended to consider more than one tail dependence measure.
4
Content available remote

On the control of the difference between two Brownian motions: a dynamic copula approach

75%
Deschatre T.
Dependence Modeling
|
2016
|
tom 4
|
nr 1
EN
We propose new copulae to model the dependence between two Brownian motions and to control the distribution of their difference. Our approach is based on the copula between the Brownian motion and its reflection. We show that the class of admissible copulae for the Brownian motions are not limited to the class of Gaussian copulae and that it also contains asymmetric copulae. These copulae allow for the survival function of the difference between two Brownian motions to have higher value in the right tail than in the Gaussian copula case. Considering two Brownian motions B1t and B2t, the main result is that the range of possible values for [...] is the same for Markovian pairs and all pairs of Brownian motions, that is [...] with φ being the cumulative distribution function of a standard Gaussian random variable.
5
Content available remote

On the control of the difference between two Brownian motions: an application to energy markets modeling

51%
Deschatre T.
Dependence Modeling
|
2016
|
tom 4
|
nr 1
EN
We derive a model based on the structure of dependence between a Brownian motion and its reflection according to a barrier. The structure of dependence presents two states of correlation: one of comonotonicity with a positive correlation and one of countermonotonicity with a negative correlation. This model of dependence between two Brownian motions B1 and B2 allows for the value of [...] to be higher than 1/2 when x is close to 0, which is not the case when the dependence is modeled by a constant correlation. It can be used for risk management and option pricing in commodity energy markets. In particular, it allows to capture the asymmetry in the distribution of the difference between electricity prices and its combustible prices.
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