Measuring the effects of reinsurance by the adjustment coefficient in the Sparre Anderson model

We study the insurer’s adjustment coefficient as a function of retention levels for combinations of quota-share with excess of loss reinsurance in the Sparre Anderson model [In: Transactions of the XV International Congress of Actuaries]. We show that the insurer’s adjustment coefficient is a unimodal function of the retention levels when the quota-share reinsurance premium is calculated on original terms and when the excess of loss premium is calculated according to the expected value principle.