Abstract

<p style='text-indent:20px;'>Consider a portfolio of <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula> losses accompanied with <inline-formula><tex-math id="M2">\begin{document}$ n $\end{document}</tex-math></inline-formula> stochastic loss adjustment factors. This paper establishes some asymptotic formulas of the tail distortion risk measure for aggregate weight-adjusted heavy-tailed losses under the framework of multivariate regular variation, pairwise quasi-asymptotic independence or arbitrary dependence. As an application, the corresponding results on the asymptotics for the risk concentration based on tail distortion risk measure are also derived. Several examples and simulation studies are provided to better illustrate the obtained results.</p>

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