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

H. Margaretha, M. Susanto, Earlitha Olivia Lionel, F. V. Ferdinand
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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 femalesStroke 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: ...
以肥胖为危险因素的中风长期护理保险精算模型
中风是一种严重的疾病,在大多数情况下会导致残疾或死亡。需要一大笔钱来支付中风病人的医疗费用。中风可侵袭所有年龄段的人,包括那些处于生育期的人。死亡和残疾无疑会给家庭带来经济负担。中风保险可以是一种长期的保障,使个人在中风或死亡时得到保护。本文采用永久性残疾收入模型对卒中保险进行建模,该模型是由健康、卒中和死亡三种状态组成的多状态模型。健康状态下的一年过渡概率由Kolmogorov正演方程的数值结果导出,而中风状态下的一年过渡概率由Poisson GLM模型计算。随后,利用Chapman-Kolmogorov方程计算了较长期跃迁概率。我们考虑了一些风险因素:年龄、性别和身体质量指数。为了得到一个适当的发病率表,我们利用了几个数据来源,即来自印度尼西亚卫生部的基础卫生研究,来自印度尼西亚中央统计局的数据,来自世界卫生组织的死亡率数据,以及来自世界银行的人口数据。结果表明,男性的净保费高于女性的中风保险提供死亡抚恤金,反之亦然,如果没有死亡抚恤金。此外,统计检验表明,肥胖显著改变了女性缴纳的保险费。中风是一种严重的疾病,在大多数情况下导致残疾或死亡。需要一大笔钱来支付中风病人的医疗费用。中风可侵袭所有年龄段的人,包括那些处于生育期的人。死亡和残疾无疑会给家庭带来经济负担。中风保险可以是一种长期的保障,使个人在中风或死亡时得到保护。本文采用永久性残疾收入模型对卒中保险进行建模,该模型是由健康、卒中和死亡三种状态组成的多状态模型。健康状态下的一年过渡概率由Kolmogorov正演方程的数值结果导出,而中风状态下的一年过渡概率由Poisson GLM模型计算。随后,利用Chapman-Kolmogorov方程计算了较长期跃迁概率。我们考虑了一些风险因素:……
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