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Stein's Lemma for elliptical random vectors

Author

Listed:
  • Landsman, Zinoviy
  • Neslehová, Johanna

Abstract

For the family of multivariate normal distribution functions, Stein's Lemma presents a useful tool for calculating covariances between functions of the component random variables. Motivated by applications to corporate finance, we prove a generalization of Stein's Lemma to the family of elliptical distributions.

Suggested Citation

  • Landsman, Zinoviy & Neslehová, Johanna, 2008. "Stein's Lemma for elliptical random vectors," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 912-927, May.
  • Handle: RePEc:eee:jmvana:v:99:y:2008:i:5:p:912-927
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    References listed on IDEAS

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    1. Mahmoud Hamada & Emiliano A. Valdez, 2008. "CAPM and Option Pricing With Elliptically Contoured Distributions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 387-409.
    2. Kenneth A. Froot, 2007. "Risk Management, Capital Budgeting, and Capital Structure Policy for Insurers and Reinsurers," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(2), pages 273-299.
    3. Landsman, Zinoviy, 2006. "On the generalization of Stein's Lemma for elliptical class of distributions," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 1012-1016, May.
    4. Owen, Joel & Rabinovitch, Ramon, 1983. " On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-752, June.
    5. Kano, Y., 1994. "Consistency Property of Elliptic Probability Density Functions," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 139-147, October.
    6. N. H. Bingham & Rudiger Kiesel, 2002. "Semi-parametric modelling in finance: theoretical foundations," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 241-250.
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    Citations

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    Cited by:

    1. Kume, Alfred & Hashorva, Enkelejd, 2012. "Calculation of Bayes premium for conditional elliptical risks," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 632-635.
    2. repec:eee:ejores:v:261:y:2017:i:2:p:606-612 is not listed on IDEAS
    3. Adcock, C J & Meade, N, 2017. "Using parametric classification trees for model selection with applications to financial risk management," European Journal of Operational Research, Elsevier, vol. 259(2), pages 746-765.
    4. Zinoviy Landsman & Udi Makov & Tomer Shushi, 2017. "Extended Generalized Skew-Elliptical Distributions and their Moments," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 76-100, February.
    5. repec:eee:stapro:v:137:y:2018:i:c:p:297-303 is not listed on IDEAS
    6. Landsman, Zinoviy & Vanduffel, Steven & Yao, Jing, 2015. "Some Stein-type inequalities for multivariate elliptical distributions and applications," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 54-62.
    7. Kumar Kattumannil, Sudheesh, 2009. "On Stein's identity and its applications," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1444-1449, June.
    8. Adcock, C.J., 2014. "Mean–variance–skewness efficient surfaces, Stein’s lemma and the multivariate extended skew-Student distribution," European Journal of Operational Research, Elsevier, vol. 234(2), pages 392-401.

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