Study on the Health-disability Transition Rates and Pricing of Health Insurance with Long-term Care in Taiwan: Using CBD-family Models

[[abstract]]本文採用健康失能和健康死亡多狀態馬可夫隨機轉換模型，用CBD家族死亡率模型(CBD、CBD-1、CBD-2和CBD-3)，logit 迴歸分析和情境分析的方法來估計台灣1970年到2009年，65歲到84歲的老年人口，在特定年齡健康失能或健康死亡轉換機率和保費計算。兩階段的估計必須一致性和漸近並且認真的執行。不同於以往的實證研究，首先考慮一個轉換機率遵循馬可夫過程。根據健康失能轉換率，女性的轉換率高於男性並且指出健康失能的轉換率逐年遞增。男性健康死亡的轉換率高於女性，轉換率逐年遞減，從而導致台灣健康死亡的風險降低。在CBD家族死亡率模型下，延伸四個模型。利用logit迴歸分析選擇最適模型，CBD-3是最佳模型。該模型表明健康失能轉換率，在特定世代縮減的世代影響下是更顯著的。更進一步證實中國人壽長期看護健康保險附約甲型、乙型和丙型保險商品組合。我們的實證發現不同市場占有率下的訂價情境分析長期看護健康保險純保費，並且填補了長期看護健康保險的多狀態精算模型從健康到失能的文獻。[[abstract]]This paper employs the stochastic model with the health-disability or the health-dead of the Markovian multi-state process in random transitions, the family of generalized CBD-Perks mortality models (CBD, CBD-1, CBD-2, and CBD-3), logit regression analysis and scenario method to estimate age-specific health-disability or health-dead transition probabilities and insurance premium among older adults aged 65 to 84 in Taiwan over 40 year 1970 to 2009. The estimation is consistent and asymptotic with a careful implementation of the two-stage method. Unlike previous empirical research, we first consider a transition probability follow a Markovian process. Based on the transition rate of health-disability, the female’s transition rate is higher than that of the male’s and indicates that health-disability transition rates are increasing by years. For the transition rate of health-dead, the male’s transition rate is higher than that of the female’s, and therefore the adverse consequences of transition rate that do occur has decreased—thus leading to lower risk in Taiwan. We then extend those four models in CBD-family mortality models and logit regression to select fitting best model and find that the model CBD-3 is the best one. The model’s results suggest that the impact of the cohort effect for a specific cohort diminishes is more significant in health-disability transition rates. This further confirms an allied line with A, B, and C types in the health insurance with long-term care of the China Life Insurance Company in Taiwan insurance market. Our empirical findings provide a basis for pure premium of long-term care insurance dependent transition rate of health-disability among older adults using scenario analysis for pricing decision in the different market share, and thus fill a gap to the literature of multi-state actuarial models of health-disability for the long-term care insurance