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Asymptotic estimates of Gerber-Shiu functions in the renewal risk model with exponential claims. (English) Zbl 1355.91049
Summary: This paper continues (cf. [Q. Tang and L. Wei, Insur. Math. Econ. 46, No. 1, 19–31 (2010; Zbl 1231.91243)]) to study the asymptotic behavior of Gerber-Shiu expected discounted penalty functions in the renewal risk model as the initial capital becomes large. Under the assumption that the claim-size distribution is exponential, we establish an explicit asymptotic formula. Some straightforward consequences of this formula match existing results in the field.
MSC:
91B30 Risk theory, insurance (MSC2010)
60K05 Renewal theory
62E20 Asymptotic distribution theory in statistics
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