THE DETERMINATION OF A PURE SINGLE PREMIUM RATE OF A CRITICAL DISEASE INSURANCE WITH MULTISTATE MODEL USING THE WEIBULL HAZARD FUNCTION: 2019 ITALY HEALTH DATA - Cindy, Felicia
A critical illness insurance is a health insurance product with benefits which will be paid in full if the policyholder is diagnosed with a critical illness stated in the contract. The transition of a person's health status can be explained using a multistate model under the assumption of a continuous time inhomogeneous Markov chain involving an estimation of transition probability. The unavailability of the incidence rate data is one of the obstacles in estimating the intensity of the transition. However, the data of the prevalence rates which are more available in practice could be used to model the transition from health to illness. In this Final Project, pure single premium will be determined for a Stand-Alone policy and for a Full Acceleration policy. In a Stand-Alone policy, benefits are paid in full if the policyholder is diagnosed with a critical illness, whereas in a Full Acceleration policy, a critical illness insurance is a rider to a life insurance policy. To determine the premium rate for each type of policies, it is necessary to estimate the transition intensity and transition probabilities. In this final project, the mortality of healthy and sick people is modeled using the Weibull hazard function. Two approaches are used to estimate the intensity of the transition, namely: the intensity of the transition which is constant in each age group; and the intensity of the transition obtained from applying a graduation method. In this final project, the graduation method used for smoothing the estimation of the transition intensity is the cubic spline method. The transition probability is calculated by numerical approximation. Finally, the resulting pure single premium rates for a Stand-Alone policy and for a Full Acceleration policy, whether obtained by using a constant transition intensity in each age group and by the smoothed transition intensity, are compared.