Canceling of Insurance Contracts

In this paper we consider an insurer who has incomplete information about the claim frequency of the risk process. He therefore calculates the premium on the basis of a prior distribution for the claim frequency. Future information might then reveal that it is no longer optimal for the insurer to continue to offer the insurance under the current conditions. We consider a model where, at certain points in time, the insurer can decide to cancel the insurance, possibly at the expense of canceling costs. The model is applicable to long-period, client tailored insurance contracts as well as insurance offered to large groups of insureds on a single period basis. We derive the optimal canceling policy and analyze the influence of the different model parameters on the expected lifetime of the insurance, the insurer’s expected surplus, and the safety loading.