Some practical applications of Sundt's (1992) generalized class of counting distributions are discussed. The numerical stabilities of some recursive formulas in Sundt's class are investigated.

In this paper we study a transform introduced by De Pril (1989) for recursive evaluation of convolutions of counting distributions with a positive probability in zero. We discuss some cases where the evaluation of this transform is simplified and relate the transform to infinitely divisible distributions. Finally we discuss an algorithm presented by Dhaene & Vandebroek (1994) for recursive evaluation of convolutions.

The set of efficient portfolios in an asset liability model is discussed in detail. The occurence of liabilities leads to a parallel shift of the efficient set. Under an appropriate assumption, the shift vector can be decomposed in different components. For the special case, where the investor is a pension fund, it is shown how shortfall constraints can be reconciled with efficiency. Finally, optimality conditions for the market portfolio are derived.

In this paper we compare ruin functions for two risk processes with respect to stochastic ordering, stop-loss ordering and ordering of adjustment coefficients. The risk processes are as follows: in the Markov-modulated environment and the associated averaged compound Poisson model. In the latter case the arrival rate is obtained by averaging over time the arrival rate in the Markov modulated model and the distribution of the claim size is obtained by averaging the ones over consecutive claim sizes.

This paper is devoted to the study of the initial reserve, as a function of the retention limit, needed to assure that the probability of ruin, at the end of a certain period of time, is not higher than an agreed value, for an excess of loss treaty. To assess the probability of ruin, the normal and the normal power approximation are used. It is shown that the initial reserve is not in general an increasing function of the retention, having a minimum under fair assumptions.