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Consider a two-dimensional renewal risk model, in which the claim sizes {X→k\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\overrightarrow{X}_{k}$$\end{document}; k ≥ 1} form a sequence of i.i.d. copies of a non-negative random vector whose two components are dependent. Suppose that the claim sizes and inter-arrival times form a sequence of i.i.d. random pairs, with each pair obeying a dependence structure via the conditional distribution of the inter-arrival time given the subsequent claim size being large. Then a precise large-deviation formula of the aggregate amount of claims is obtained.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Aug 5, 2021
Keywords: consistent variation; extended regular variation; large deviations; size-dependence; two-dimensional risk model; 60F10; 91B30; 60K05
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