Multitype Negative Risk Sums

In insurance terminology there are only two kinds of risk insurance which are positive risk sums and negative risk sums. The ruin probability \Psi(u) for a Poisson model of multitype negative risk sums is mainly studied in the paper. We prove that the Lundberg inequality on the ruin probability for the model is held, that is, \Psi(u) ≤C_e^-R_u. In the-case where the time intervals of size fluctuations are bounded, we prove that \Psi(u) = e^-R_u, which is the generalization of the corresponding result on the classical negative risk sums.