Ruin probabilities in multivariate risk models with periodic common shock

Ionica Cojocaru

Scandinavian Actuarial Journal, 2017, vol. 2017, issue 2, 159-174

Abstract: 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.

Date: 2017
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DOI: 10.1080/03461238.2015.1094404

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