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Asymptotic behaviour of the finite-time ruin probability under subexponential claim sizes. (English) Zbl 1183.91073
Summary: The paper deals with the Sparre Andersen risk model. We study the tail behaviour of the finite-time ruin probability, $$\Psi (x,t)$$, in the case of subexponential claim sizes as initial risk reserve $$x$$ tends to infinity. The asymptotic formula holds uniformly for $$t$$ in a corresponding region and reestablishes a formula of Q. Tang [Stoch. Models 20, No. 3, 281–297 (2004; Zbl 1130.60312)] obtained for the class of claim distributions having consistent variation.

##### MSC:
 91B30 Risk theory, insurance (MSC2010) 60K05 Renewal theory 60K10 Applications of renewal theory (reliability, demand theory, etc.)
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