# Precise Large Deviations for Sums of Claim-size Vectors in a Two-dimensional Size-dependent Renewal Risk Model

Precise Large Deviations for Sums of Claim-size Vectors in a Two-dimensional Size-dependent... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# Precise Large Deviations for Sums of Claim-size Vectors in a Two-dimensional Size-dependent Renewal Risk Model

, Volume 37 (3) – Aug 5, 2021
9 pages

/lp/springer-journals/precise-large-deviations-for-sums-of-claim-size-vectors-in-a-two-TrU4LyUGvD
Publisher
Springer Journals
Copyright © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2021
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-021-1030-z
Publisher site
See Article on Publisher Site

### Abstract

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.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Aug 5, 2021

Keywords: consistent variation; extended regular variation; large deviations; size-dependence; two-dimensional risk model; 60F10; 91B30; 60K05

### References

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