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

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