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Bernstein Approximations to the Copula Function and Portfolio Optimization

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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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    References listed on IDEAS

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    1. Kon, Stanley J, 1984. "Models of Stock Returns-A Comparison," Journal of Finance, American Finance Association, vol. 39(1), pages 147-165, March.
    2. Phillips, Peter C B, 1983. "ERAs: A New Approach to Small Sample Theory," Econometrica, Econometric Society, vol. 51(5), pages 1505-1525, September.
    3. Nelsen, Roger B., 1997. "Dependence and Order in Families of Archimedean Copulas," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 111-122, January.
    4. Karim Abadir, 1999. "An introduction to hypergeometric functions for economists," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 287-330.
    5. Joe, H., 1993. "Parametric Families of Multivariate Distributions with Given Margins," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 262-282, August.
    6. 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.
    7. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    8. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
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    Citations

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    Cited by:

    1. Paula V. Tofoli & Flavio A. Ziegelmann & Osvaldo Candido, 2017. "A Comparison Study of Copula Models for Europea Financial Index Returns," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 9(10), pages 155-178, October.
    2. 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.
    3. Ines Fortin & Christoph Kuzmics, 2002. "Tail‐dependence in stock‐return pairs," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 11(2), pages 89-107, April.
    4. Szego, Giorgio, 2005. "Measures of risk," European Journal of Operational Research, Elsevier, vol. 163(1), pages 5-19, May.
    5. Chadwick, Meltem Gulenay, 2019. "Dependence of the “Fragile Five” and “Troubled Ten” emerging market financial systems on US monetary policy and monetary policy uncertainty," Research in International Business and Finance, Elsevier, vol. 49(C), pages 251-268.
    6. Sancetta, A., 2005. "Copula Based Monte Carlo Integration in Financial Problems," Cambridge Working Papers in Economics 0506, Faculty of Economics, University of Cambridge.
    7. 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.

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    More about this item

    Keywords

    copulae; Bernstein polynomials; approximation theory; portfolio;
    All these keywords.

    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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