A multivariate aggregate loss model

In this paper, we introduce a multivariate aggregate loss model, where multiple categories of losses are considered. The model assumes that different types of claims arrive according to a Marked Markovian arrival process (MMAP) introduced by He and Neuts (1998) in the queuing literature. This approach enables us to allow dependencies among the claim frequencies, and among the claim sizes, as well as between claim frequencies and claim sizes. This model extends the (univariate) Markov modulated risk processes (sometimes referred to as regime switching models) widely used in insurance and financial analysis. For the proposed model, we provide formulas for calculating the joint moments of the present value of aggregate claims occurring in any time interval (0,t]. Numerical examples are provided to show possible applications of the model.