Convex combinations of quadrant dependent copulas

Martín Egozcue; Luis Fuentes García; Wing Keung Wong; Ričardas Zitikis

doi:10.1016/j.aml.2012.08.019

Convex combinations of quadrant dependent copulas

Martín Egozcue^*, Luis Fuentes García, Wing Keung Wong, Ričardas Zitikis

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › peer-review

13 Citations (Scopus)

Abstract

It is well known that quadrant dependent (QD) random variables are also quadrant dependent in expectation (QDE). Recent literature has offered examples rigorously establishing the fact that there are QDE random variables which are not QD. The examples are based on convex combinations of specially chosen QD copulas: one negatively QD and another positively QD. In this paper we establish general results that determine when convex combinations of arbitrary QD copulas give rise to negatively or positively QD/QDE copulas. In addition to being an interesting mathematical exercise, the established results are helpful when modeling insurance and financial portfolios.

Original language	English
Pages (from-to)	249-251
Number of pages	3
Journal	Applied Mathematics Letters
Volume	26
Issue number	2
DOIs	https://doi.org/10.1016/j.aml.2012.08.019
Publication status	Published - Feb 2013

Scopus Subject Areas

Applied Mathematics

User-Defined Keywords

Convex combination
Copula
Quadrant dependence
Quadrant dependence in expectation

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10.1016/j.aml.2012.08.019

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title = "Convex combinations of quadrant dependent copulas",

abstract = "It is well known that quadrant dependent (QD) random variables are also quadrant dependent in expectation (QDE). Recent literature has offered examples rigorously establishing the fact that there are QDE random variables which are not QD. The examples are based on convex combinations of specially chosen QD copulas: one negatively QD and another positively QD. In this paper we establish general results that determine when convex combinations of arbitrary QD copulas give rise to negatively or positively QD/QDE copulas. In addition to being an interesting mathematical exercise, the established results are helpful when modeling insurance and financial portfolios.",

keywords = "Convex combination, Copula, Quadrant dependence, Quadrant dependence in expectation",

author = "Mart{\'i}n Egozcue and {Fuentes Garc{\'i}a}, Luis and Wong, {Wing Keung} and Ri{\v c}ardas Zitikis",

note = "Funding Information: We are grateful to an anonymous referee for suggestions that have aided us when revising the paper. This project is a part of our research under the grant FRG1/10- 11/012 from Hong Kong Baptist University (HKBU) entitled “The Covariance Sign of Transformed Random Variables with Applications to Economics, Finance and Insurance.” We also gratefully acknowledge our research support by the Agencia Nacional de Investigaci{\'o}n e Innovaci{\'o}n (ANII) of Uruguay , the Research Grants Council (RGC) of Hong Kong , and the Natural Sciences and Engineering Research Council (NSERC) of Canada .",

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doi = "10.1016/j.aml.2012.08.019",

language = "English",

volume = "26",

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AU - Egozcue, Martín

AU - Fuentes García, Luis

AU - Wong, Wing Keung

AU - Zitikis, Ričardas

N1 - Funding Information: We are grateful to an anonymous referee for suggestions that have aided us when revising the paper. This project is a part of our research under the grant FRG1/10- 11/012 from Hong Kong Baptist University (HKBU) entitled “The Covariance Sign of Transformed Random Variables with Applications to Economics, Finance and Insurance.” We also gratefully acknowledge our research support by the Agencia Nacional de Investigación e Innovación (ANII) of Uruguay , the Research Grants Council (RGC) of Hong Kong , and the Natural Sciences and Engineering Research Council (NSERC) of Canada .

PY - 2013/2

Y1 - 2013/2

N2 - It is well known that quadrant dependent (QD) random variables are also quadrant dependent in expectation (QDE). Recent literature has offered examples rigorously establishing the fact that there are QDE random variables which are not QD. The examples are based on convex combinations of specially chosen QD copulas: one negatively QD and another positively QD. In this paper we establish general results that determine when convex combinations of arbitrary QD copulas give rise to negatively or positively QD/QDE copulas. In addition to being an interesting mathematical exercise, the established results are helpful when modeling insurance and financial portfolios.

AB - It is well known that quadrant dependent (QD) random variables are also quadrant dependent in expectation (QDE). Recent literature has offered examples rigorously establishing the fact that there are QDE random variables which are not QD. The examples are based on convex combinations of specially chosen QD copulas: one negatively QD and another positively QD. In this paper we establish general results that determine when convex combinations of arbitrary QD copulas give rise to negatively or positively QD/QDE copulas. In addition to being an interesting mathematical exercise, the established results are helpful when modeling insurance and financial portfolios.

KW - Convex combination

KW - Copula

KW - Quadrant dependence

KW - Quadrant dependence in expectation

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U2 - 10.1016/j.aml.2012.08.019

DO - 10.1016/j.aml.2012.08.019

M3 - Journal article

AN - SCOPUS:84867849769

SN - 0893-9659

VL - 26

SP - 249

EP - 251

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 2

ER -

Convex combinations of quadrant dependent copulas

Abstract

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