On Multidimensional Risk Models with Lower and Upper Barriers

We consider a risk model with n classes of business with claim counting Poisson processes. We assume that the dividends are paid because of the presence of a reflecting upper barrier and, to avoid ruin, we consider dynamic solvency insurance contracts that depend on a given definition of time of ruin. We describe a fairly general model and, under various assumptions, we find the equations fulfilled by the discounted dividend payments and by the net single premium of dynamic solvency insurance. We provide explicit solutions in the special case of exponential distribution and numerical examples to highlight the effect of some parameters’ variation on the values of the discounted value of dividend payments.