Joint moments of discounted compound renewal sums

Ghislain Léveillé, Franck Adékambi

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


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 languageEnglish
Pages (from-to)40-55
Number of pages16
JournalScandinavian Actuarial Journal
Issue number1
Publication statusPublished - Mar 2012
Externally publishedYes


  • 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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