Asymptotic behaviour of the finite‐time ruin probability in renewal risk models |
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Authors: | Remigijus Leipus Jonas ?iaulys |
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Institution: | 1. Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius LT‐03225, Lithuania;2. Institute of Mathematics and Informatics, Akademijos 4, Vilnius LT‐08663, Lithuania |
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Abstract: | 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. |
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Keywords: | insurance risk ruin probability renewal risk model strongly subexponential distribution |
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