On the Assessment of the Payment Limitation for an Health Plan

The study deals with the assessment of an optimal reimbursement strategy for an Health Plan, that covers several branches of disease (e.g. surgery, orthodontia, diagnostic tests, medical devices etc.). We start from the estimation of the expected value and variance of the health expenditure for each branch by a three-part regression model, based on Generalized Linear Models (GLM). Then, we define a reimbursement rule (e.g. deductibles, co-payments, policy limits etc.) by means of the ratio between the per payment values (reimbursement) and the per loss values (expenditure). The latter is the proportion of expenditure reimbursed and is defined as Indicated Deductible Relativity (IDR); an IDR is calculated for each branch covered by the Health Plan. We apply the optimization problem proposed by De Finetti (1940) in the context of proportional reinsurance to calculate the IDR values, that minimize the variance of the total reimbursement of the Health Plan fixing the expected total gain. Furthermore, an application is provided for an italian Health Plan in case of uncorrelated branches.