General methods for bounding multidimensional ruin probabilities in regime-switching models

We present a universal methodology for bounding multidimensional ultimate ruin probabilities Psi in regime-switching models. Some new lower and upper bounds on Psi are given. The considered methods are applicable to several discrete- and continuous time risk models. As an example, we construct a variety of new two-sided operator bounds which converge to Psi with an exponential rate. Several numerical examples are also provided.