The purpose of this note is two-fold. First we derive a simple condition under which two s-convex ordered random variables must be stochastically equal, and we indicate the potential usefulness of this result in statistics. Then we highlight the relationship between the canonical moments and the...

This note discusses a simple quasi-Monte Carlo method to evaluate numerically the ultimate ruin probability in the classical compound Poisson risk model. The key point is the Pollaczek-Khintchine representation of the non-ruin probability as a series of convolutions. Our suggestion is to...

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...