Critical illness insurance with a hidden Markov model

In the literature, multi-state models are used in the calculations on critical illness insurance. In these models, in which the critical illness incidence rates are estimated, covariates can only be included after splitting into different group combinations due to the constraints of the method. This situation causes the data to be divided into too many sub-risk groups, inability to use continuous covariates and restriction in the validity of the results to a particular number of groups. In this thesis it is aimed to propose a model that can be used in the pricing of critical illness insurance and considers the risk groups with a holistic perspective. For this purpose, using Hidden Markov Models (HMM) in modeling critical illness insurances is proposed. Incidence rates of critical illnesses are estimated for different risk groups with HMM. This thesis uses the longitudinal panel data collected in The Health and Retirement Study (HRS) by Michigan University Social Research Institute. Using HRS data, parameters of both HMM and the orthodox models in the literature are estimated and their performances are compared. Results indicate that in most of the scenarios, the HMM model proposed in the thesis performs better than the Markov Model whose parameters are computed using Generalized Linear Model. Furthermore, premium calculations are done using Thiele's differential equation and simulation method.