Uzun Dönem Bakım Sigortasında Uzun Ömürlülük Riskinin Fiyatlandırılması

Abstract

An increase in the incidence and duration of chronic illnesses have occurred with the extension of the expected life span. Chronic diseases lead to deterioration of the physical condition of the patients. These disorders cause individuals to be unable to meet their daily needs and the quality of life to deteriorate. The patient needs other a person or people to meet their daily needs. Life expectancy in Turkey is increasing. Expected increase in life expectancy will increase the demand for care services. Increasing demand will put pressure on the state budget. As a solution to this problem long-term care insurance models should be developed for older people.

Long-term care insurance is usually modeled with simple Markov, which is a single state for dependency. But the degree of disease for elderly individuals vary from day to day. The degree of disease affects the duration in dependency. Therefore, it is inadequate to explain in a single situation the duration in state of dependency. In this study, the long-term care insurance model, which is in the literature, has been adapted to Turkey. The state of dependency is divided into four according to the degree of dependency and the transition probabilities are assumed to be semi-Markov process. Transition possibilities in the semiMarkov process are not only dependent on the current state, but also on the duration of the present state.

The Cox proportional hazard model was used to explain the duration of dependency, with age and gender explanatory variables. It is also thought that the types of disease affects the duration in dependency. But, frailty model that can not be observed because there is no information about the types of diseases is used. Parameter estimation is performed with duration of dependency model which is mention above.

For the duration of dependency, parameter values existing in the literature are used. The life span of healthy individuals for [40,60] age range was estimated by Monte Carlo simulation using the general mortality rate in Turkey and the incidence rate of France becoming in dependency from a healthy state. Two scenarios were simulated. The first scenario is based on the assumption that the probability of death does not change over time, and the second scenario is based on the assumption that the probability of death changes every year depending on the risk of longevity. For both scenarios, premiums and reserves for each age are calculated by cash flow method. Mortality rate and rate of becoming dependent is examined effect on premium of long term care insurance.

Keywords: Long-Term Care Insurance, Longevity Risk, Monte Carlo Simulation Method, Censoring, Cox Proportional Hazard Model, Frailty Model, Generalized Linear Model