In the collective risk model we use the objective Bayesian approach to calculate predictive aggregate claims distributions. Very often this is equivalent to the profile predictive likelihood approach, but the former is more straightforward to apply, and accordingly we use it as a pragmatic device

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We present two approaches how to find the distribution law for the aggregate claims in given insurance portfolio. We assume that a book of policies is the union of disjoint classes and each of which has an aggregate distribution. The formulas for the aggregate claims for the whole book are applied

We introduce a simple aggregate claims model, which is able to take into account a continuous range of positive dependence between independence and comonotone dependence. It is based on a multivariate extension of the one-parameter bivariate Fréchet copula, which finds a justification as follows

In this paper we study the eect of dierent dependence structures on the distribution of total losses when the reinsurer undertakes excess of loss for two or more dependent portfolios. We also study the asymptotic behaviour of the joint distribution of the reinsurance aggregate claim amounts

ABSTRACT A formula, originally presented by HALDANE (1938) 2, for the evaluation of the distribution of aggregate claims is examined and compared with some other approaches. The idea is to apply a symmetrizing transformation to the original variable m order to make it suscepuble to be approximated

In this paper an algorithm is derived for computing the distribution of aggregate claims for the individual risk theory model. The procedure is an adaptation of the recursive method used in the solution of ordinary differential equations. Mathematical arguments are deliberately kept

In the present paper we discuss error bounds for approximations to aggregate claims distributions. We consider approximations to convolutions by approx-imating each of the distributions and taking the convolution of these approximations. For compound distributions we consider two classes

. Furthermore an integral representation for the tail of compound sums of Pareto-distributed claims is obtained and numerical illustrations of its performance in comparison to other aggregate claim approximations are provided. 1

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.