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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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