Asymptotic behavior of ruin probabilities in a multidimensional risk model with investment and multivariate regularly varying claims

Yang, Yang; Qi, Shihua

doi:10.1016/j.jmaa.2023.127319

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2024

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“…The only established class of multivariate heavy-tailed distributions is that of multivariate regular variation. This class was already used in risk theory and risk management, see for example [34], [56], [41] and [42]. In bigger distribution classes, there were several attempts for definitions of multivariate subexponential distributions, see [13], [47], [48].…”

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confidence: 99%

On the non-closure under convolution for strong subexponential distributions

Konstantinides

Leipus²,

Šiaulys³

2022

NAMC

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In this paper, we consider the convolution closure problem for the class of strong subexponential distributions, denoted as S*. First, we show that, if F, G ∈ L, then inclusions of F*G, FG, and pF + (1 – p)G for all (some) p ∈ (0; 1) into the class S* are equivalent. Then, using examples constructed by Klüppelberg and Villasenor [The full solution of the convolution closure problem for convolution-equivalent distributions, J. Math. Anal. Appl., 41:79–92, 1991], we show that S* is not closed under convolution.

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