Asymptotic results for heavy-tailed distributions using defective renewal equations

Georgios Psarrakos

Statistics & Probability Letters, 2009, vol. 79, issue 6, 774-779

Abstract: In this note, we investigate the asymptotic behavior of two special functions that satisfy defective renewal equations and have a key role in risk theory. Heavy-tailed distributions are important in our analysis. Furthermore, applying our results to the renewal and classical models of risk theory yields a generalisation of a well-known asymptotic formula of [Embrechts, P., Veraverbeke, N., 1982. Estimates for the probability of ruin with special emphasis on the possibility of large claims. Insurance Math. Econom. 1, 55-72].

Date: 2009
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