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South African Actuarial Journal

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Linear predictor of the discounted renewal aggregate claims with dependent inter-occurrence times

F Adékambi

Abstract


In this paper we derive the first two moments and a linear predictor of the compound discounted renewal aggregate claims when taking into account dependence within the inter-occurrence times. Using specific mixtures of exponential distributions to define the dependence structure between the inter-occurrence times, we compare the accuracy of the proposed linear predictor to the simulated value of that sum.

Keywords: Discounted compound renewal aggregate sums; moments; Archimedean copula; random interest rate; linear predictor




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