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Joint moments of discounted compound renewal sums

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  • Ghislain Léveillé
  • Franck Adékambi

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.

Suggested Citation

  • Ghislain Léveillé & Franck Adékambi, 2012. "Joint moments of discounted compound renewal sums," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2012(1), pages 40-55.
    • Handle: RePEc:taf:sactxx:v:2012:y:2012:i:1:p:40-55
    DOI: 10.1080/03461238.2010.503426
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