Precise large deviations of aggregate claims in a risk model with regression-type size-dependence

In this note, we further extend the renewal risk model and introduce a more practical regression-type dependence structure between inter-arrival times and claim sizes, which is described by the framework of a web Markov skeleton process. We investigate large deviations of the aggregate claims, and,...

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Bibliographic Details
Published in:Statistics & probability letters 2013-10, Vol.83 (10), p.2248-2255
Main Authors: Bi, Xiuchun, Zhang, Shuguang
Format: Article
Language:English
Subjects:
Aggregate claims
Consistent variation
Dependence
Large deviations
Web Markov skeleton process
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Summary:In this note, we further extend the renewal risk model and introduce a more practical regression-type dependence structure between inter-arrival times and claim sizes, which is described by the framework of a web Markov skeleton process. We investigate large deviations of the aggregate claims, and, for a case of heavy-tailed claims, we obtain a precise large-deviation formula of the aggregate claims under some assumption about regression-type size-dependence, which is consistent with existing ones in the literature.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2013.06.009