Optimal Bounds for Integrals with Respect to Copulas and Applications

Optimal Bounds for Integrals with Respect to Copulas and Applications

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Article ID: iaor2014766
Volume: 161
Issue: 3
Start Page Number: 999
End Page Number: 1011
Publication Date: Jun 2014
Journal: Journal of Optimization Theory and Applications
Authors: ,
Keywords: approximation, generalised assignment, copulas
Abstract:

We consider the integration of two‐dimensional, piecewise constant functions with respect to copulas. By drawing a connection to linear assignment problems, we can give optimal upper and lower bounds for such integrals and construct the copulas for which these bounds are attained. Furthermore, we show how our approach can be extended in order to approximate extremal values in very general situations. Finally, we apply our approximation technique to problems in financial mathematics and uniform distribution theory, such as the model‐independent pricing of first‐to‐default swaps.

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