Pricing in general insurance with non-constant deductibles in claim cost distributions

Abstract

The collective risk theory establishes that the calculation of the pure premium in general insurance is obtained as the product of the expected values of the random variables representing the number of claims and the cost of claims, which together constitute the compound variable generating the aggregate claims process. This estimator for the pure premium is feasible due to the assumption that the number of claims and the cost of claims are independent random variables, and that claim costs, when exceeding one claim, are mutually independent and identically distributed. If the assumption of identical distributions for claim costs is relaxed—that is, if claim costs are no longer assumed to be identically distributed—the estimator for the pure premium would change. From this new model, actuarial applications for pricing can be derived by incorporating stochastic deductibles, these deductibles can vary for each claim allowing more flexibility to the pricing process.