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On the Gerber-Shiu discounted penalty function for subexponential claims. (English) Zbl 1131.60080
Lith. Math. J. 46, No. 4, 487-493 (2006); and Liet. Mat. Rink. 46, No. 4, 598-605 (2006).
Summary: We obtain the asymptotics of the H. U. Gerber and E. S. W. Shiu [N. Am. Actuar. J. 2, No. 1, 48–78 (1998; Zbl 1081.60550)] discounted penalty function in the classical Lundberg model. We consider claims from a class of subexponential distributions and find the asymptotics as the initial surplus $$x$$ tends to infinity. The main term of the discounted penalty function $$\psi (x, \delta)$$ has different expressions in the cases where the interest rate $$\delta > 0$$ and where $$\delta = 0$$.

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