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1
Content available remote

Quantile of a Mixture with Application to Model Risk Assessment

100%
Bernard C., Vanduffel S.
Dependence Modeling
|
2015
|
tom 3
|
nr 1
EN
We provide an explicit expression for the quantile of a mixture of two random variables. The result is useful for finding bounds on the Value-at-Risk of risky portfolios when only partial dependence information is available. This paper complements the work of [4].
2
Content available remote

On the k-gamma q-distribution

76%
Díaz R., Ortiz C., Pariguan E.
Open Mathematics
|
2010
|
tom 8
|
nr 3
448-458
EN
We provide combinatorial as well as probabilistic interpretations for the q-analogue of the Pochhammer k-symbol introduced by Díaz and Teruel. We introduce q-analogues of the Mellin transform in order to study the q-analogue of the k-gamma distribution.
3
Content available remote

Some applications of the Archimedean copulas in the proof of the almost sure central limit theorem for ordinary maxima

76%
Dudziński M., Furmańczyk K.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1024-1034
EN
Our goal is to state and prove the almost sure central limit theorem for maxima (Mn) of X1, X2, ..., Xn, n ∈ ℕ, where (Xi) forms a stochastic process of identically distributed r.v.’s of the continuous type, such that, for any fixed n, the family of r.v.’s (X1, ...,Xn) has the Archimedean copula CΨ.
4
Content available remote

Bivariate copulas, norms and non-exchangeability

76%
Papini P. L.
Dependence Modeling
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2015
|
tom 3
|
nr 1
EN
The present paper is related to the study of asymmetry for copulas by introducing functionals based on different norms for continuous variables. In particular, we discuss some facts concerning asymmetry and we point out some flaws occurring in the recent literature dealing with this matter.
5
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CMPH: a multivariate phase-type aggregate loss distribution

64%
Ren J., Zitikis R.
Dependence Modeling
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2017
|
tom 5
|
nr 1
304-315
EN
We introduce a compound multivariate distribution designed for modeling insurance losses arising from different risk sources in insurance companies. The distribution is based on a discrete-time Markov Chain and generalizes the multivariate compound negative binomial distribution, which is widely used for modeling insurance losses.We derive fundamental properties of the distribution and discuss computational aspects facilitating calculations of risk measures of the aggregate loss, as well as allocations of the aggregate loss to individual types of risk sources. Explicit formulas for the joint moment generating function and the joint moments of different loss types are derived, and recursive formulas for calculating the joint distributions given. Several special cases of particular interest are analyzed. An illustrative numerical example is provided.
6
Content available remote

An analysis of the Rüschendorf transform - with a view towards Sklar’s Theorem

64%
Oertel F.
Dependence Modeling
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2015
|
tom 3
|
nr 1
EN
We revisit Sklar’s Theorem and give another proof, primarily based on the use of right quantile functions. To this end we slightly generalise the distributional transform approach of Rüschendorf and facilitate some new results including a rigorous characterisation of an almost surely existing “left-invertibility” of distribution functions.
7
Content available remote

Dependent defaults and losses with factor copula models

52%
Ackerer D., Vatter T.
Dependence Modeling
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2017
|
tom 5
|
nr 1
375-399
EN
We present a class of flexible and tractable static factor models for the term structure of joint default probabilities, the factor copula models. These high-dimensional models remain parsimonious with paircopula constructions, and nest many standard models as special cases. The loss distribution of a portfolio of contingent claims can be exactly and efficiently computed when individual losses are discretely supported on a finite grid. Numerical examples study the key features affecting the loss distribution and multi-name credit derivatives prices. An empirical exercise illustrates the flexibility of our approach by fitting credit index tranche prices.
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