Locally and globally uniform approximations for ruin probabilities of a nonstandard bidimensional risk model with subexponential claims

Consider a nonstandard continuous-time bidimensional risk model with constant force of interest, in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent. Under some mild condit...

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Bibliographic Details
Published in:Applied Mathematics-A Journal of Chinese Universities 2024-03, Vol.39 (1), p.98-113
Main Authors: Liu, Zai-ming, Geng, Bing-zhen, Wang, Shi-jie
Format: Article
Language:English
Subjects:
Applications of Mathematics
Approximation
Mathematical analysis
Mathematics
Mathematics and Statistics
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Summary:Consider a nonstandard continuous-time bidimensional risk model with constant force of interest, in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent. Under some mild conditions, we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval. If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed, it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.
ISSN:1005-1031
1993-0445
DOI:10.1007/s11766-024-4213-6