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

Yang Yang, Eglė Ignatavičiūtė and Jonas Šiaulys

Statistics & Probability Letters, 2015, vol. 105, issue C, 20-28

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.

Keywords: Randomly weighted sum; Heavy-tailed distribution; Sarmanov copula; Conditional tail expectation (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (6)

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DOI: 10.1016/j.spl.2015.05.016

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