Some Results on Bivariate Compound Poisson Risk Model

In this paper we consider a risk model with two correlated classes of insurance business. Asymptotic results for the deficit at ruin caused by different classes of insurance business are obtained. Explicit expression for the deficit at ruin caused by different classes of insurance business are given when the original claim size random variables are exponentially distributed. In addition we also give a brief discussion on the classical risk model perturbed by the Gamma process.