Abstract
Formulas have been obtained for the moments of the discounted aggregate claims process, for a constant instantaneous interest rate, and for a claims number process that is an ordinary or a delayed renewal process. In this paper, we present explicit formulas on the first two moments and the joint moment of this risk process, for a non-trivial extension to a stochastic instantaneous interest rate. Examples are given for Erlang claims number processes, and for the Ho-Lee-Merton and the Vasicek interest rate models.
| Original language | English |
|---|---|
| Pages (from-to) | 138-153 |
| Number of pages | 16 |
| Journal | Scandinavian Actuarial Journal |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Jun 2011 |
| Externally published | Yes |
Keywords
- Asymptotic and finite time moments
- Discounted aggregate claims
- Itô process
- Joint moments
- Renewal process
- Stochastic interest rate
ASJC Scopus subject areas
- Statistics and Probability
- Economics and Econometrics
- Statistics, Probability and Uncertainty