The Annals of Applied Probability

An extension to the renewal theorem and an application to risk theory

H. Schmidli

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Abstract

In applied probability one is often interested in the asymptotic behavior of a certain quantity. If a regenerative phenomenon can be imbedded, then one has the problem that the event of interest may have occurred but cannot be observed at the renewal points. In this paper an extension to the renewal theorem is proved which shows that the quantity of interest converges. As an illustration an open problem in risk theory is solved.

Article information

Source
Ann. Appl. Probab. Volume 7, Number 1 (1997), 121-133.

Dates
First available in Project Euclid: 14 October 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1034625255

Digital Object Identifier
doi:10.1214/aoap/1034625255

Mathematical Reviews number (MathSciNet)
MR1428752

Zentralblatt MATH identifier
0876.60072

Subjects
Primary: 60K05: Renewal theory
Secondary: 60F10: Large deviations 62P05: Applications to actuarial sciences and financial mathematics

Keywords
Renewal theorem limit theorems large deviations risk theory ruin probabilities

Citation

Schmidli, H. An extension to the renewal theorem and an application to risk theory. Ann. Appl. Probab. 7 (1997), no. 1, 121--133. doi:10.1214/aoap/1034625255. https://projecteuclid.org/euclid.aoap/1034625255


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