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: | Hofer Markus, Iac Maria |
Keywords: | approximation, generalised assignment, copulas |
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.