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An iterative algorithm to bound partial moments

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  • Sander Muns

    (Tilburg University, Netspar)

Abstract

This paper presents an iterative algorithm that bounds the lower and upper partial moments of an arbitrary univariate random variable X by using the information contained in a sequence of finite moments of X. The obtained bounds on the partial moments imply bounds on the moments of the transformation f(X) for a certain function $$f:\mathbb {R}\rightarrow \mathbb {R}$$ f : R → R . Two examples illustrate the performance of the algorithm.

Suggested Citation

  • Sander Muns, 2019. "An iterative algorithm to bound partial moments," Computational Statistics, Springer, vol. 34(1), pages 89-122, March.
    • Handle: RePEc:spr:compst:v:34:y:2019:i:1:d:10.1007_s00180-018-0825-8
    DOI: 10.1007/s00180-018-0825-8
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    References listed on IDEAS

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    1. Gwo Dong Lin, 1997. "On the moment problems," Statistics & Probability Letters, Elsevier, vol. 35(1), pages 85-90, August.
    2. Bawa, Vijay S. & Lindenberg, Eric B., 1977. "Abstract: Capital Market Equilibrium in a Mean-Lower Partial Moment Framework," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 635-635, November.
    3. Karl Frauendorfer, 1988. "Solving SLP Recourse Problems with Arbitrary Multivariate Distributions---The Dependent Case," Mathematics of Operations Research, INFORMS, vol. 13(3), pages 377-394, August.
    4. Steftcho P. Dokov & David P. Morton, 2005. "Second-Order Lower Bounds on the Expectation of a Convex Function," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 662-677, August.
    5. Jan R. Magnus, 1986. "The Exact Moments of a Ratio of Quadratic Forms in Normal Variables," Annals of Economics and Statistics, GENES, issue 4, pages 95-109.
    6. Robert L. Winkler & Gary M. Roodman & Robert R. Britney, 1972. "The Determination of Partial Moments," Management Science, INFORMS, vol. 19(3), pages 290-296, November.
    7. Bawa, Vijay S. & Lindenberg, Eric B., 1977. "Capital market equilibrium in a mean-lower partial moment framework," Journal of Financial Economics, Elsevier, vol. 5(2), pages 189-200, November.
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