Ruin Probabilities for One Class of Bivariate Risk Model with Correlated Aggregate Claims under Sparse Processes

The paper considers a risk model with two dependent classes of insurance business. In this model, the two claim number processes are partly sparsely correlated through an Erlang(2) process. By introducing an auxiliary model, we obtain the integral equations for ultimate ruin probabilities, and discuss the asymptotic property of ruin probabilities by renewal approach. We also get the linear differential equations of ruin probabilities of the model and the corresponding auxiliary model when claims follow the exponential distributions, and show how solves the linear differential equations by a specific example.