Covariance of discounted compound renewal sums with a stochastic interest rate |
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Authors: | Ghislain Léveillé Franck Adékambi |
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Affiliation: | 1. école d'actuariat , Université Laval , QC, Canada ghislain.leveille@act.ulaval.ca;3. école d'actuariat , Université Laval , QC, Canada |
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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. |
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Keywords: | Asymptotic and finite time moments Discounted aggregate claims Itô process Stochastic interest rate Joint moments Renewal process |
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