An actuarial model of stroke long term care insurance with obesity as a risk factor

Abstract

Stroke is a critical illness that causes disability or death in most cases. A considerable amount of money is needed to cover the medical cost of a stroke patient. Stroke can attack people of all ages, including those who are at productive periods. Death and disability will undoubtedly cause a financial burden to the family. Stroke insurance can be a long-term guarantee so that individuals are protected when they suffered from a stroke or died. In this paper, stroke insurance was modeled with a permanent disability income model, which is a multiple state model consisting of three states: healthy, stroke, and death. One-calendar year transition probabilities from the healthy state were derived from the numerical results of the Kolmogorov forward equations, while one-calendar year transition probabilities from the stroke state were calculated by using a Poisson GLM model. Afterwards, longer-term transition probabilities were calculated using the Chapman-Kolmogorov equation. We considered some risk factors: age, gender, and body mass index. In order to get a proper morbidity table, we utilized several sources of data, namely, the Basic Health Research from the Indonesia Ministry of Health, data from the Indonesia Central Statistical Bureau, the mortality data from the World Health Organization, and the population data from the World Bank. The results obtained showed that the net premium is higher for males than for females for stroke insurance providing a death benefit, and vice versa if there is no death benefit. Furthermore, statistical tests showed that being obese significantly changes the insurance premium paid by females.