Abstract: Erlangian risk model is widely used in queueing theory,control theory and finance risk models.Under the assumptions that the claim-arrival follows Erlangian process,the claim-size is Paretian distributed and the constant interest force exists,this paper obtains the asymptotic formula of finite-time ruin probability,that essentially extends the corresponding results of reference^[1] which only deals with ultimate time ruin probability,and reference^[2] which merely limits the model to the Poisson case.By the relationship between ruin model and queueing model we know that the results we obtain can be applied to management science in many aspects.

Key words: Erlangian risk model, finite time ruin probabilities, constant interest force, Pareto-type claim-size