Abstract
The first two moments and the covariance of the aggregate discounted claims have been found for a stochastic interest rate, from which the inflation rate has been subtracted, and for a claims number process that is an ordinary or a delayed renewal process.Hereafter we extend the preceding results by presenting recursive formulas for the joint moments of this risk process, for a constant interest rate, and non-recursive formulas for higher joint moments when the interest rate is stochastic. Examples are given for exponential claims inter-arrival times and for the Ho-Lee-Merton interest rate model.
| Original language | English |
|---|---|
| Pages (from-to) | 40-55 |
| Number of pages | 16 |
| Journal | Scandinavian Actuarial Journal |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Mar 2012 |
| Externally published | Yes |
Keywords
- 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