In this paper, we investigate asymptotic properties of the tail probabilities of the maxima of partial sums of independent random variables. For some large classes of heavy-tailed distributions, we show that the tail probabilities of the maxima of the partial sums asymptotically equal to the sum...

A method for analysing the risk of taking a too low reserve level by the use of Chain Ladder method is developed. We give an answer to the question of how much safety loading in terms of the Chain Ladder standard error has to be added to the Chain Ladder reserve in order to reach a specified...

We reconsider the problem of producing fair and accurate tariffs based on aggregated insurance data giving numbers of claims and total costs for the claims. Jorgensen and de Souza (Scand. Actuarial J., 1994) assumed Poisson arrival of claims and gamma distributed costs for individual claims....