THE DETERMINATION OF A PURE SINGLE PREMIUM RATE OF A CRITICAL DISEASE INSURANCE WITH A MULTISTATE MODEL USING THE GOMPERTZ HAZARD FUNCTION: 2019 ITALY HEALTH DATA - Muhamad Fathan Al Badri, Faiq
A critical illness insurance is a health insurance which provide benefit if the insured suffers a critical illness during the period of the policy. A critical illness insurance policy could be in the form of a Stand-Alone policy which pay a lump sum benefit if the insured is diagnosed with a critical illness; or a Full Acceleration policy in which the critical illness insurance is a rider to a life insurance policy. With the Full Acceleration policy, the benefit could be paid if the insured is diagnosed with a critical illness or if the insured dies. In this final project, a multistate model is used under the assumption that the Markov chain is not homogeneous with continuous time to determine the price of critical illness insurance premiums. The multistate model involves estimating the intensity of the transition and the probability of the transition. To build a multistate model of a critical illness insurance, incidence rate data is needed. However, due to the unavailability of such data, the data of prevalence rates could be used to model the transition from health to illness. In this final project, the Gompertz hazard function is used to model the mortality of healthy people and sick people. Then, a graduation method is used to smooth the initial estimation results of the transition intensity while a numerical approach is used to calculate the transition probability. A pure single premium rate is determined for a Critical Illness Stand Alone policy and a Critical Illness Full Acceleration policy. The pure single premium rates for both policies are then compared between those using the smoothed transition intensities and those using the transition intensities before the graduation method is applied.