The purpose of this paper is to point out that an asymptotic rule "A+B/u" for the ultimate ruin probability applies to a wide class of dependent risk models, in discrete and continuous time. Dependence is incorporated through a mixing approach among claim amounts or claim inter-arrival times,...

In risk management, the distribution of underlying random variables is not always known. Sometimes, only the mean value and some shape information (decreasingness, convexity after a certain point,...) of the discrete density are available. The present paper aims at providing convex extrema in...

This paper is concerned with the compound Poisson risk model and two generalized models with still Poisson claim arrivals. One extension incorporates inhomogeneity in the premium input and in the claim arrival process, while the other takes into account possible dependence between the successive...

In the compound Poisson risk model, several strong hypotheses may be found too restrictive to describe accurately the evolution of the reserves of an insurance company. This is especially true for a company that faces natural disaster risks like earthquake or flooding. For such risks, claim...

In the renewal risk model, several strong hypotheses may be found too restrictive to model accurately the complex evolution of the reserves of an insurance company. In the case where claim sizes are heavy-tailed, we relax independence and stationarity assumptions and extend some asymptotic...

The present paper aims to point out how the stationary-excess operator and its iterates transform the s-convex stochastic orders and the associated moment spaces. This allows us to propose a new unified method on constructing s-convex extrema for distributions that are known to be t-monotone....

This paper is concerned with the class of distributions, continuous or discrete, whose shape is monotone of finite integer order t. A characterization is presented as a mixture of a minimum of t independent uniform distributions. Then, a comparison of t-monotone distributions is made using the...

The purpose of this paper is to point out that an asymptotic rule "A+B/u" for the ultimate ruin probability applies to a wide class of dependent risk models, in discrete and continuous time. Dependence is incorporated through a mixing approach among claim amounts or claim inter-arrival times,...

The present paper aims to point out how the stationary-excess operator and its iterates transform s-convex stochastic orders and the associated moment spaces. This allows us to propose a new unified method on constructing s-convex extrema for distributions that are known to be t-monotone. Both...

In the renewal risk model, several strong hypotheses may be found too restrictive to model accurately the complex evolution of the reserves of an insurance company. In the case where claim sizes are heavy-tailed, we relax the independence and stationarity assumptions and extend some asymptotic...