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Bounds on Capital Requirements For Bivariate Risk with Given Marginals and Partial Information on the Dependence

Bounds on Capital Requirements For Bivariate Risk with Given Marginals and Partial Information on... AbstractNelsen et al. [20] find bounds for bivariate distribution functions when there are constraints on the values of its quartiles. Tankov [25] generalizes this work by giving explicit expressionsfor the best upper and lower bounds for a bivariatecopula when its values on a compact subset of [0; 1]2are known. He shows that they are quasi-copulas and notnecessarily copulas. Tankov [25] and Bernard et al. [3] bothgive sufficient conditions for these bounds to be copulas. Inthis note we give weaker sufficient conditions to ensure thatboth bounds are simultaneously copulas. Furthermore, wedevelop a novel application to quantitative risk managementby computing bounds on a bivariate risk measure. This canbe useful in optimal portfolio selection, in reinsurance, in pricingbivariate derivatives or in determining capital requirementswhen only partial information on dependence is available. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Dependence Modeling de Gruyter

Bounds on Capital Requirements For Bivariate Risk with Given Marginals and Partial Information on the Dependence

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Publisher
de Gruyter
Copyright
©2013 Versita Sp. z o.o.
ISSN
2300-2298
eISSN
2300-2298
DOI
10.2478/demo-2013-0002
Publisher site
See Article on Publisher Site

Abstract

AbstractNelsen et al. [20] find bounds for bivariate distribution functions when there are constraints on the values of its quartiles. Tankov [25] generalizes this work by giving explicit expressionsfor the best upper and lower bounds for a bivariatecopula when its values on a compact subset of [0; 1]2are known. He shows that they are quasi-copulas and notnecessarily copulas. Tankov [25] and Bernard et al. [3] bothgive sufficient conditions for these bounds to be copulas. Inthis note we give weaker sufficient conditions to ensure thatboth bounds are simultaneously copulas. Furthermore, wedevelop a novel application to quantitative risk managementby computing bounds on a bivariate risk measure. This canbe useful in optimal portfolio selection, in reinsurance, in pricingbivariate derivatives or in determining capital requirementswhen only partial information on dependence is available.

Journal

Dependence Modelingde Gruyter

Published: Jan 1, 2013

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