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Conditional tail expectation of randomly weighted sums with heavy-tailed distributions

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  • Yang, Yang
  • Ignatavičiūtė, Eglė
  • Šiaulys, Jonas

Abstract

We consider the tail behavior of the conditional tail expectation E(Snθ∣Snθ>xq) when q↑1. Here Snθ=∑i=1nθiXi and xq=VaRq(Snθ)=inf{y∈R:P(Snθ⩽y)⩾q}. We are interested in the case when the primary random variables X1,X2,…,Xn are real-valued and regularly varying, while the random weights θ1,θ2,…,θn are nonnegative and not degenerate at zero. We suppose that random vectors (X1,θ1),(X2,θ2),…(Xn,θn) are independent, while Xk and θk follow a certain dependence structure. We also present the related asymptotic results, some of which hold if distribution functions of X1,X2,…,Xn are long tailed and dominatingly varying.

Suggested Citation

  • Yang, Yang & Ignatavičiūtė, Eglė & Šiaulys, Jonas, 2015. "Conditional tail expectation of randomly weighted sums with heavy-tailed distributions," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 20-28.
    • Handle: RePEc:eee:stapro:v:105:y:2015:i:c:p:20-28
    DOI: 10.1016/j.spl.2015.05.016
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    Cited by:

    1. Mantas Dirma & Saulius Paukštys & Jonas Šiaulys, 2021. "Tails of the Moments for Sums with Dominatedly Varying Random Summands," Mathematics, MDPI, vol. 9(8), pages 1-26, April.
    2. Katleho Makatjane, 2022. "Forecasting Uncertainty Intervals for Return Period of Extreme Daily Electricity Consumption," International Journal of Energy Economics and Policy, Econjournals, vol. 12(4), pages 217-225, July.
    3. Landsman, Zinoviy & Makov, Udi & Shushi, Tomer, 2016. "Tail conditional moments for elliptical and log-elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 179-188.
    4. Xing-Fang Huang & Ting Zhang & Yang Yang & Tao Jiang, 2017. "Ruin Probabilities in a Dependent Discrete-Time Risk Model With Gamma-Like Tailed Insurance Risks," Risks, MDPI, vol. 5(1), pages 1-14, March.
    5. Gustas Mikutavičius & Jonas Šiaulys, 2023. "Product Convolution of Generalized Subexponential Distributions," Mathematics, MDPI, vol. 11(1), pages 1-11, January.
    6. Jaunė, Eglė & Šiaulys, Jonas, 2022. "Asymptotic risk decomposition for regularly varying distributions with tail dependence," Applied Mathematics and Computation, Elsevier, vol. 427(C).

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