Fair Actuarial Values for Deductible Insurance Policies in the Presence of Parameter Uncertainty

Abstract

This paper derives the multi-period fair actuarial values for six deductible insurance policies offered in today's insurance markets. The loss in any given period is generated by the Weibull distribution with a known shape parameter but an unknown scale parameter. The insurer is assumed to be a Bayesian decision maker, in the sense that he/she learns sequentially about the unknown scale parameter by observing the realizations of the filed claims. It is shown that the insurer's underlying predictive loss distributions belong to the Burr family, and the multi-period actuarially fair policy value can be derived. With a proper loading, an insurance premium can be quoted. Our major contribution is the analytical derivations of the fair actuarial values for deductible insurance policies in the presence of parameter uncertainty and Bayesian learning.