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Bernstein Approximations to the Copula Function and Portfolio Optimization

Author

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  • A. Sancetta
  • Satchell, S.E.

Abstract

The copula function is considered within the context of financial multivariate data sets that are not normally distributed. The Bernstein polynomial approximation to copulae is given and motivated by its desirable properties. The multivariate convergence properties are analysed. The concept of Bernstein copula is introduced as a generalisation of some bivariate and higher dimensional families of copulae. Statistical properties of the Bernstein copula are studied together with implementation issues related to portfolio theory and expected utility optimisation.

Suggested Citation

  • A. Sancetta & Satchell, S.E., 2001. "Bernstein Approximations to the Copula Function and Portfolio Optimization," Cambridge Working Papers in Economics 0105, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:0105
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    File URL: http://www.econ.cam.ac.uk/research-files/repec/cam/pdf/wp0105.pdf
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    References listed on IDEAS

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    1. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," Review of Economic Studies, Oxford University Press, vol. 25(2), pages 65-86.
    2. Karim Abadir, 1999. "An introduction to hypergeometric functions for economists," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 287-330.
    3. Hagerman, Robert L, 1978. "More Evidence on the Distribution of Security Returns," Journal of Finance, American Finance Association, vol. 33(4), pages 1213-1221, September.
    4. Phillips, Peter C B, 1983. "ERAs: A New Approach to Small Sample Theory," Econometrica, Econometric Society, vol. 51(5), pages 1505-1525, September.
    5. Nelsen, Roger B., 1997. "Dependence and Order in Families of Archimedean Copulas," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 111-122, January.
    6. Joe, H., 1993. "Parametric Families of Multivariate Distributions with Given Margins," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 262-282, August.
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    Citations

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    Cited by:

    1. Alessio Sancetta, 2004. "Copula Based Monte Carlo Integration in Financial Problems," Working Papers wp04-02, Warwick Business School, Finance Group.
    2. Szego, Giorgio, 2002. "Measures of risk," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1253-1272, July.
    3. Romera, Rosario & Molanes, Elisa M., 2008. "Copulas in finance and insurance," DES - Working Papers. Statistics and Econometrics. WS ws086321, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Fortin, Ines & Kuzmics, Christoph, 2002. "Tail-Dependence in Stock-Return Pairs," Economics Series 126, Institute for Advanced Studies.
    5. Alessio Sancetta & Steve E. Satchell, 2007. "Changing Correlation and Equity Portfolio Diversification Failure for Linear Factor Models during Market Declines," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(3), pages 227-242.

    More about this item

    Keywords

    copulae; Bernstein polynomials; approximation theory; portfolio;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other

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