文章基本信息

标题：Bounds on Capital Requirements For Bivariate Risk with Given Marginals and Partial Information on the Dependence
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作者：Carole Bernard ; Yuntao Liu ; Niall MacGillivray 等
期刊名称：Dependence Modeling
电子版ISSN：2300-2298
出版年度：2013
卷号：1
DOI：10.2478/demo-2013-0002
语种：English
出版社：Walter de Gruyter GmbH
摘要：Nelsen et al. [20] find bounds for bivariate distribution functionswhen 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.
关键词：Copulas; Fréchet-Hoeffding bounds; Capital requirements