AGGREGATE CLAIMS DEPENDENCE MODEL BASED ON GENERALIZED LINEAR MODELS AND ITS APPLICATION USING UTILITY THEORY FOR COORDINATION OF BENEFITS SCHEME OF BPJS KESEHATAN - Koerniawan, Vieri
This Thesis discusses the modeling of aggregate claims consisting of claim frequency and severity components. The random variable of claim frequency and severity can be derived from the exponential dispersion family (EDF) distribution. If there are observations with a zero value whose proportion is too high for the claim frequency, the zero inflated distribution is used as an alternative. In general, the claim frequency and severity components are assumed to be independent. However, this Thesis explores aggregate claim modeling that assumes the dependence between the frequency and severity of claims using the generalized linear models (GLM) approach. With this dependency assumption, the claim severity is considered as a random variable that depends on the claim frequency, and is referred to as conditional claim severity. The GLM is used to model the marginal claim frequency and conditional claim severity. The results from the model of marginal claim frequency are then used as new parameters to generate random values. This random value is used as an additional covariate in modeling conditional claim severity based on Monte Carlo simulations. The marginal claim frequency and conditional claim severity model results are used to form the claim aggregate dependency model. The resulting aggregate claims dependence model is applied to BPJS Kesehatan claims data, especially with catastrophic disease diagnoses. In the data analysis process, a sub-portfolio was created based on the BPJS Kesehatan care class category, consisting of three classes. The degree of dependence obtained from the conditional severity model parameters estimation showed significant results for Class II, whereas for Class I and Class III, it was not significant. The resulting degree of dependence parameter for Class II has a negative value, while for Class I and Class III has a positive value. The expected value of aggregate claims resulting from Class II by including the dependency assumption is of lower value if without the dependency assumption. The opposite applies to the expected value results of aggregate claims in Class I and Class III. Thus, it can be said that the assumption of dependence affects the expected value of the aggregate claims obtained. The expected value of the aggregate claims obtained is used to design a coordination of benefits (CoB) scheme with utility theory. This Thesis introduces a new CoB scheme in which BPJS Kesehatan shares a portion of the claim burden based on a certain cost sharing proportion to private health insurance (PHI) with the quota share concept. The optimal proportion of cost sharing is determined by maximizing the utility of BPJS Kesehatan and PHI. Through maximum utility, a premium model is produced which will be offered to participants by PHI. The modeled premium is smaller than the participant's out-of-pocket payment (OOP) when compared to the risk of additional claims that are not covered by BPJS Kesehatan.