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Asymptotics for the ruin probabilities of a two‐dimensional renewal risk model with heavy‐tailed claims
Author(s) -
Chen Yiqing,
Yuen Kam C.,
Ng Kai W.
Publication year - 2010
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.834
Subject(s) - ruin theory , mathematics , risk model , type (biology) , renewal theory , first hitting time model , risk process , feature (linguistics) , mathematical economics , econometrics , actuarial science , statistics , economics , philosophy , ecology , linguistics , biology
In this paper, we consider two dependent classes of insurance business with heavy‐tailed claims. The dependence comes from the assumption that claim arrivals of the two classes are governed by a common renewal counting process. We study two types of ruin in the two‐dimensional framework. For each type of ruin, we establish an asymptotic formula for the finite‐time ruin probability. These formulae possess a certain uniformity feature in the time horizon. Copyright © 2010 John Wiley & Sons, Ltd.