## The Annals of Applied Probability

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

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

#### 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**

http://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. http://projecteuclid.org/euclid.aoap/1034625255.