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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access December 31, 2013

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

  • Carole Bernard EMAIL logo , Yuntao Liu , Niall MacGillivray and Jinyuan Zhang
From the journal Dependence Modeling

Abstract

Nelsen 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 expressions for the best upper and lower bounds for a bivariate copula when its values on a compact subset of [0; 1]2 are known. He shows that they are quasi-copulas and not necessarily copulas. Tankov [25] and Bernard et al. [3] both give sufficient conditions for these bounds to be copulas. In this note we give weaker sufficient conditions to ensure that both bounds are simultaneously copulas. Furthermore, we develop a novel application to quantitative risk management by computing bounds on a bivariate risk measure. This can be useful in optimal portfolio selection, in reinsurance, in pricing bivariate derivatives or in determining capital requirements when only partial information on dependence is available.

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Received: 2013-05-05
Accepted: 2013-10-08
Published Online: 2013-12-31
Published in Print: 2013-01-01

©2013 Versita Sp. z o.o.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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