Covariance of discounted compound renewal sums with a stochastic interest rate

Ghislain Léveillé, Franck Adékambi

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


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 languageEnglish
Pages (from-to)138-153
Number of pages16
JournalScandinavian Actuarial Journal
Issue number2
Publication statusPublished - Jun 2011
Externally publishedYes


  • 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


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