Ruin probabilities in multivariate risk models with periodic common shock

We propose a multidimensional risk model where the common shock affecting all classes of insurance business is arriving according to a non-homogeneous periodic Poisson process. In this multivariate setting, we derive upper bounds of Lundberg-type for the probability that ruin occurs in all classes simultaneously using the martingale approach via piecewise deterministic Markov processes theory. These results are numerically illustrated in a bivariate risk model, where the beta-shape periodic claim intensity function is considered. Under the assumption of dependent heavy-tailed claims, asymptotic bounds for the finite-time ruin probabilities associated to three types of ruin in this multivariate framework are investigated.