Covariance of discounted compound renewal sums with a stochastic interest rate

Ghislain Léveillé and Franck Adékambi

Scandinavian Actuarial Journal, 2011, vol. 2011, issue 2, 138-153

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.

Date: 2011
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DOI: 10.1080/03461231003665632

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