A New Look at the Adjustment Coefficient in theCompound Poisson Model Perturbed by Diffusion

In this paper, we study the adjustment coefficient as a function of the retention levels for combinations of quota-share with excess of loss reinsurance in the compound Poisson model perturbed by diffusion. We calculate the quota-share on original terms and the excess of loss reinsurance premium according to the expected value principle. Then the result that the adjustment coefficient is a unimodal function of the retention limit for excess of loss reinsurance in this risk model is obtained. In the last part of this paper, an upper bound for the probability of ruin in finite horizon is given.