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Optimal Bounds for Integrals with Respect to Copulas and Applications

Author

Listed:
  • Markus Hofer

    (Graz University of Technology)

  • Maria Rita Iacò

    (Graz University of Technology
    University of Calabria)

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.

Suggested Citation

  • Markus Hofer & Maria Rita Iacò, 2014. "Optimal Bounds for Integrals with Respect to Copulas and Applications," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 999-1011, June.
    • Handle: RePEc:spr:joptap:v:161:y:2014:i:3:d:10.1007_s10957-013-0454-x
    DOI: 10.1007/s10957-013-0454-x
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    References listed on IDEAS

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    1. Christoph Aistleitner & Markus Hofer & Robert Tichy, 2012. "A Central Limit Theorem For Latin Hypercube Sampling With Dependence And Application To Exotic Basket Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(07), pages 1-20.
    2. Packham, Natalie & Schmidt, Wolfgang M., 2008. "Latin hypercube sampling with dependence and applications in finance," CPQF Working Paper Series 15, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    3. Puccetti, Giovanni, 2013. "Sharp bounds on the expected shortfall for a sum of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1227-1232.
    4. Peter Tankov, 2010. "Improved Frechet bounds and model-free pricing of multi-asset options," Papers 1004.4153, arXiv.org, revised Mar 2011.
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