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Bernstein Approximations to the Copula Function and Portfolio Optimization

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Author Info
A. Sancetta
Satchell, S.E.

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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.

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File URL: http://www.econ.cam.ac.uk/dae/repec/cam/pdf/wp0105.pdf
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Publisher Info
Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 0105.

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Length: 47
Date of creation: Jun 2001
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Handle: RePEc:cam:camdae:0105

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Related research
Keywords: copulae; Bernstein polynomials; approximation theory; portfolio;

Find related papers by JEL classification:
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other

This paper has been announced in the following NEP Reports:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. James Tobin, 1956. "Liquidity Preference as Behavior Towards Risk," Cowles Foundation Discussion Papers 14, Cowles Foundation, Yale University. [Downloadable!]
  2. Karim Abadir, 1999. "An introduction to hypergeometric functions for economists," Econometric Reviews, Taylor and Francis Journals, vol. 18(3), pages 287-330. [Downloadable!] (restricted)
    Other versions:
  3. Hagerman, Robert L, 1978. "More Evidence on the Distribution of Security Returns," Journal of Finance, American Finance Association, vol. 33(4), pages 1213-21, September. [Downloadable!] (restricted)
  4. Nelsen, Roger B., 1997. "Dependence and Order in Families of Archimedean Copulas," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 111-122, January. [Downloadable!] (restricted)
  5. Phillips, Peter C B, 1983. "ERAs: A New Approach to Small Sample Theory," Econometrica, Econometric Society, vol. 51(5), pages 1505-25, September. [Downloadable!] (restricted)
    Other versions:
  6. Joe, H., 1993. "Parametric Families of Multivariate Distributions with Given Margins," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 262-282, August. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Sancetta, A., 2005. "Copula Based Monte Carlo Integration in Financial Problems," Cambridge Working Papers in Economics 0506, Faculty of Economics, University of Cambridge. [Downloadable!]
  2. Fortin, Ines & Kuzmics, Christoph, 2002. "Tail-Dependence in Stock-Return Pairs," Economics Series 126, Institute for Advanced Studies. [Downloadable!]
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