Premium adjustment: actuarial analysis on epidemiological models

Abstract

In this paper, we analyse insurance premium adjustment in the context of an epidemiological model where the insurer’s future financial liability is greater than the premium from patients. In this situation, it becomes extremely difficult for the insurer since a negative reserve would severely increase its risk of insolvency, or might cause bankruptcy. This situation might also make many policy holders withdraw from the insurance by simply terminating their premium payments. It is proved that the benefit
reserve changes from negative to positive and from concave to convex under the condition stated in Proposition 5.3 of this paper. As the premium tends to optimum premium rate, the local maximum in the first arch approaches the local minimum in the second arch and they all converge at a time point tm. As a result, the reserve benefit shifts upwards as the premium rate increases. It is concluded that a proper premium rate between initial and optimum premium rates exist in order to fulfil certain reserves requirements and an algorithm to determine this value was developed.