Evaluating risk measures, premiums, and capital allocation based on dependent multi-losses is a notoriously difficult task. In this paper, we demonstrate how this can be successfully accomplished when losses follow the multivariate Pareto distribution of the second kind, which is an attractive...

In the present paper, we study error bounds for approximations to multivariate distributions. In particular, we discuss some general versions of compound multivariate distributions and look at distributions of dependent random variables constructed by linear transforms of independent random...

We present an algorithm for recursive evaluation of the corresponding...

Prediction is a very important and not so easy task for an actuary. An insurance company needs predictions of the future claims in order to evaluate premiums, to assess its financial situation, probabilities of ruin, etc. Therefore, modeling the claims distribution is of great importance, but...

Starting from the question: “What is the accident risk of an insured?”, this paper considers a multivariate approach by taking into account three types of accident risks and the possible dependence between them. Driven by a real data set, we propose three trivariate Sarmanov distributions...

In this paper, we extend the class of bivariate Sarmanov distributions by introducing some bivariate mixed Sarmanov distributions. Special attention is paid to the bivariate mixed Sarmanov distribution with Poisson marginals and, in particular, to the resulting bivariate Sarmanov distribution...

Based on many numerical examples, Raducan et al. (2015b) stated a conjecture that relates the order in which some nonhomogeneous claims arrive to the magnitude of the corresponding ruin probability. In that conjecture, the usual stochastic order has been considered for the claims. However, in...