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In this paper, we consider a class of bidimensional discrete-time risk models, which are based on the assumptions that the claim counts obey some specific bivariate integer-valued time series such as bivariate Poisson MA (BPMA) and the bivariate Poisson AR (BPAR) processes. We derive the moment generating functions (m.g.f.’s) for these processes, and we present their explicit expressions for the adjustment coefficient functions. The asymptotic approximations (upper bounds) to three different types of ruin probabilities are discussed, and the marginal value-at-risk (VaR) for each model is obtained. Numerical examples are provided to compute the adjustment coefficients discussed in the paper.

Bidimensional discrete-time risk models based on bivariate claim count time series