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1
Content available remote

Multivariate measures of concordance for copulas and their marginals

100%
Taylor M. D.
Dependence Modeling
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2016
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tom 4
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nr 1
EN
Building upon earlier work in which axioms were formulated for multivariate measures of concordance, we examine properties of such measures. In particular,we examine the relations between the measure of concordance of an n-copula and the measures of concordance of the copula’s marginals.
2
Content available remote

Measuring herd behavior: properties and pitfalls

100%
Lee W., Ahn J. Y.
Dependence Modeling
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2017
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tom 5
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nr 1
316-329
EN
Herd behavior is an important economic phenomenon, especially in the context of the recent financial crises. Prior studies propose several measures to quantify herd behavior. In this paper, we show that these measures reflect different perspectives on this behavior, and hence, their interpretation requires great care. Taking a critical attitude toward existing herd behavior measures, we study their properties and pitfalls in detail.
3
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A two-component copula with links to insurance

100%
Ismail S., Yu G., Reinert G., Maynard T.
Dependence Modeling
|
2017
|
tom 5
|
nr 1
295-303
EN
This paper presents a new copula to model dependencies between insurance entities, by considering how insurance entities are affected by both macro and micro factors. The model used to build the copula assumes that the insurance losses of two companies or lines of business are related through a random common loss factor which is then multiplied by an individual random company factor to get the total loss amounts. The new two-component copula is not Archimedean and it extends the toolkit of copulas for the insurance industry.
4
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Multivariate Markov Families of Copulas

100%
Overbeck L., Schmidt W. M.
Dependence Modeling
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2015
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tom 3
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nr 1
EN
For the Markov property of a multivariate process, a necessary and suficient condition on the multidimensional copula of the finite-dimensional distributions is given. This establishes that the Markov property is solely a property of the copula, i.e., of the dependence structure. This extends results by Darsow et al. [11] from dimension one to the multivariate case. In addition to the one-dimensional case also the spatial copula between the different dimensions has to be taken into account. Examples are also given.
5
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Band copulas as spectral measures for two-dimensional stable random vectors

88%
Bojarski J., K. Misiewicz J.
Discussiones Mathematicae Probability and Statistics
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2003
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tom 23
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nr 1
69-75
EN
In this paper, we study basic properties of symmetric stable random vectors for which the spectral measure is a copula, i.e., a distribution having uniformly distributed marginals.
6
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Inference for copula modeling of discrete data: a cautionary tale and some facts

88%
Faugeras O. P.
Dependence Modeling
|
2017
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tom 5
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nr 1
121-132
EN
In this note, we elucidate some of the mathematical, statistical and epistemological issues involved in using copulas to model discrete data. We contrast the possible use of (nonparametric) copula methods versus the problematic use of parametric copula models. For the latter, we stress, among other issues, the possibility of obtaining impossible models, arising from model misspecification or unidentifiability of the copula parameter.
7
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Quantifying the impact of different copulas in a generalized CreditRisk+framework An empirical study

75%
Jakob K., Fischer M.
Dependence Modeling
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2014
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tom 2
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nr 1
EN
Without any doubt, credit risk is one of the most important risk types in the classical banking industry. Consequently, banks are required by supervisory audits to allocate economic capital to cover unexpected future credit losses. Typically, the amount of economical capital is determined with a credit portfolio model, e.g. using the popular CreditRisk+ framework (1997) or one of its recent generalizations (e.g. [8] or [15]). Relying on specific distributional assumptions, the credit loss distribution of the CreditRisk+ class can be determined analytically and in real time. With respect to the current regulatory requirements (see, e.g. [4, p. 9-16] or [2]), banks are also required to quantify how sensitive their models (and the resulting risk figures) are if fundamental assumptions are modified. Against this background, we focus on the impact of different dependence structures (between the counterparties of the bank’s portfolio) within a (generalized) CreditRisk+ framework which can be represented in terms of copulas. Concretely, we present some results on the unknown (implicit) copula of generalized CreditRisk+ models and quantify the effect of the choice of the copula (between economic sectors) on the risk figures for a hypothetical loan portfolio and a variety of parametric copulas.
8
Content available remote

Nonparametric estimation of simplified vine copula models: comparison of methods

75%
Nagler T., Schellhase C., Czado C.
Dependence Modeling
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2017
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tom 5
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nr 1
99-120
EN
In the last decade, simplified vine copula models have been an active area of research. They build a high dimensional probability density from the product of marginals densities and bivariate copula densities. Besides parametric models, several approaches to nonparametric estimation of vine copulas have been proposed. In this article, we extend these approaches and compare them in an extensive simulation study and a real data application. We identify several factors driving the relative performance of the estimators. The most important one is the strength of dependence. No method was found to be uniformly better than all others. Overall, the kernel estimators performed best, but do worse than penalized B-spline estimators when there is weak dependence and no tail dependence.
9
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Markov morphisms: a combined copula and mass transportation approach to multivariate quantiles

63%
Faugeras O. P., Rüschendorf L.
Mathematica Applicanda
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2017
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tom 45
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nr 1
PL
W artykule zaproponowano pewien sposobu wprowadzania kwantyli wielowymiarowych, jak i metody ich wyznaczania. Z jednej strony podstawą rozważań są podstawowe własności uogólnionego pojęcia wielowymiarowego kwantyla, który jest morfizmem markowskiem, zachowującym podobne własności algebraiczne, topologiczne oraz porządku, jakie znamy dla linii kwantylowych na prostej rzeczywistej. Z drugiej zaś strony, zaproponowano morfiz markowski, który łączy standaryzowaną kopułę (funkcję łącznikową) z zastosowaniem  zagadnienia transportowego (v. Chernozhukov et al.(2017)). Proponowane podejście daje ogólne i jednolite podejście do definicji kwantyli i ich estymacji, zarówno dla ciągłych, jak i dyskretnych rozkładów wielowymiarowych.
EN
Our purpose is both conceptual and practical. On the one hand, we discuss the question which properties are basic ingredients of a general conceptual notion of a multivariate quantile. We propose and argue that the object “quantile” should be defined as a Markov morphism which carries over similar algebraic, ordering and topological properties as known for quantile functions on the real line. On the other hand, we also propose a practical quantile Markov morphism which combines a copula standardization and the recent optimal mass transportation method of Chernozhukov et al. (2015). Its empirical counterpart has the advantages of being a bandwidth-free, monotone invariant, a.s. consistent transformation. The proposed the approach gives a general and unified framework to quantiles and their corresponding depth areas, for both a continuous or a discrete multivariate distribution.
10
Content available remote

A joint regression modeling framework for analyzing bivariate binary data in R

63%
Marra G., Radice R.
Dependence Modeling
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2017
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tom 5
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nr 1
268-294
EN
We discuss some of the features of the R add-on package GJRM which implements a flexible joint modeling framework for fitting a number of multivariate response regression models under various sampling schemes. In particular,we focus on the case inwhich the user wishes to fit bivariate binary regression models in the presence of several forms of selection bias. The framework allows for Gaussian and non-Gaussian dependencies through the use of copulae, and for the association and mean parameters to depend on flexible functions of covariates. We describe some of the methodological details underpinning the bivariate binary models implemented in the package and illustrate them by fitting interpretable models of different complexity on three data-sets.
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