×

zbMATH — the first resource for mathematics

The use of Archimedian copulas to model portfolio allocations. (English) Zbl 1072.91022
Summary: A copula is a means of generating an \(n\)-variate distribution function from an arbitrary set of n univariate distributions. For the class of portfolio allocators that are risk averse, we use the copula approach to identify a large set of \(n\)-variate asset return distributions such that the relative magnitudes of portfolio shares can be ordered according to the reversed hazard rate ordering of the \(n\) underlying univariate distributions. We also establish conditions under which first- and second-degree dominating shifts in one of the \(n\) underlying univariate distributions increase allocation to that asset. Our findings exploit separability properties possessed by the Archimedean family of copulas.

MSC:
91B28 Finance etc. (MSC2000)
PDF BibTeX Cite
Full Text: DOI
References:
[1] M. M. Ali, J. Multivar. Anal. 8 pp 405– (1978)
[2] S. Athey (1998 ): Characterizing Properties of Stochastic Objective Functions . Unpublished manuscript, Massachusetts Institute of Technology, April.
[3] Cook R. D., J. Royal Stat. Soc. B 43 pp 210– (1981)
[4] P. Embrechts, A. J. McNeil, and D. Straumann (1999 ): Correlation and Dependence in Risk Management: Properties and Pitfalls .Unpublished manuscript, Department of Mathematics, Swiss Federal Institute of Technology, Zurich, July.
[5] Frank M. J., Aequationes Math 19 pp 194– (1979)
[6] R. Frey, A. J. McNeil, and M. A. Nyfeler (2001 ): Modelling Dependent Defaults; Asset Correlations Are Not Enough . Unpublished manuscript, Swiss Banking Institute, University of Zurich, March.
[7] Genest C., Am. Statistician 40 pp 280– (1986)
[8] Hadar J., Inter. Econ. Rev. 31 pp 721– (1990)
[9] Jouini M. N., Oper. Res. 44 pp 444– (1996)
[10] DOI: 10.1023/A:1004918708964 · Zbl 0893.90014
[11] Kijima, Math. Finance 6 pp 237– (1996)
[12] L. Klecan, R. McFadden, and D. McFadden (1991 ): A Robust Test for Stochastic Dominance . Unpublished manucript, Massachusetts Institute of Technology, January.
[13] Landsberger M., J. Econ. Theory 50 pp 204– (1990)
[14] Li D. X., J. Fixed Income 43 pp 43– (2000)
[15] Marshall A. W., J. Amer. Stat. Assoc. 83 pp 834– (1988)
[16] McEntire P. L., Mgmt. Sci. 30 pp 952– (1984)
[17] Meyer J., Inter. Econ. Rev. 35 pp 603– (1994)
[18] Mitchell D. E., Inter. Econ. Rev. 38 pp 945– (1997)
[19] DOI: 10.1006/jmva.1996.1646 · Zbl 0883.62049
[20] Nelsen R. B., An Introduction to Copulas (1999)
[21] Shaked M., Stochastic Orders and Their Applications (1994) · Zbl 0806.62009
[22] Sklar A., Publication of the Institute of Statistics, University of Paris 8 pp 229– (1959)
[23] Wolff E. F., Stochastica 4 pp 175– (1981)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.