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Asymptotic behaviour of the finite‐time ruin probability in renewal risk models
Author(s) -
Leipus Remigijus,
Šiaulys Jonas
Publication year - 2008
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.747
Subject(s) - infinity , mathematics , risk model , ruin theory , class (philosophy) , mathematical economics , first hitting time model , combinatorics , statistics , mathematical analysis , computer science , artificial intelligence
In this paper we study the tail behaviour of the probability of ruin within finite time t , as initial risk reserve x tends to infinity, for the renewal risk model with strongly subexponential claim sizes. The asymptotic formula holds uniformly for t ∈[ f ( x ), ∞), where f ( x ) is an infinitely increasing function, and substantially extends the result of Tang ( Stoch. Models 2004; 20 :281–297) obtained for the class of claim distributions with consistently varying tails. Two examples illustrate the result. Copyright © 2008 John Wiley & Sons, Ltd.