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Stein’s lemma for truncated elliptical random vectors

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  • Shushi, Tomer

Abstract

In this letter we derive the multivariate Stein’s lemma for truncated elliptical random vectors. The results in this letter generalize Stein’s lemma for elliptical random vectors given in Landsman and Nešlehová (2008), and the tail Stein’s lemma given in Landsman and Valdez (2016). We give a conditional Stein’s-type inequalities and a conditional version of Siegel’s formula for the elliptical distributions, and by that we generalize results obtained in Landsman et al. (2013) and in Landsman et al. (2015). Furthermore, we show applications of the main results in the letter for risk theory.

Suggested Citation

  • Shushi, Tomer, 2018. "Stein’s lemma for truncated elliptical random vectors," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 297-303.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:297-303
    DOI: 10.1016/j.spl.2018.02.008
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    References listed on IDEAS

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    1. Landsman, Zinoviy, 2004. "On the generalization of Esscher and variance premiums modified for the elliptical family of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 563-579, December.
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    Cited by:

    1. Shushi, Tomer, 2019. "The Minkowski length of a spherical random vector," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 104-107.
    2. Tomer Shushi, 2018. "Towards a Topological Representation of Risks and Their Measures," Risks, MDPI, vol. 6(4), pages 1-11, November.

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