Health Transition Probability and Long-Term Care Cost Estimation

Abstract

The cost of long-term care (LTC) is one of the huge financial risks faced by the elderly and also is a significant challenge to the social security system. This article establishes a piecewise constant Markov model to estimate the dynamic health transition probability and based on actuarial theory to calculate the long-term care cost, in contrast to the static or nontransferable state hypotheses in traditional models. Using the Chinese Longitudinal Healthy Longevity Survey, this article found that the average cost of LTC for the elderly varies greatly due to gender and health conditions, the cost for women may increase by up to 75% compared to that for men, and the cost for unhealthy elderly may more than double compared to that for healthy elderly. Furthermore, if LTC is included in the medical insurance system, in theory, women's average pay price will be more than twice that of men.

Analyzing the demographic coherence of selected US, Australian and Chinese biometric data sets used to price long-term care insurance and life care annuities

“…There is more divergence in the time that active people are likely to spend in a state of dependence. In the Cui et al (2022) model, active life expectancy is 52.26 and 36.86% of total life expectancy for males and females respectively, whereas Jiao (2019) and Zhen et al (2022) report a range of values between 86.60 and 94.60% for males and 89.44 and 96.53% for females as a proportion of total life expectancy.…”

“…Despite the fact that all the biometric data sets we have analysed have their own problems, we would say that the most coherent from a demographic/epidemiological standpoint are those in Hariyanto et al (2014a, b) and Robinson (1996). On the basis of all the information we have analysed, the data set with the most consistency problems would be Cui et al (2022).…”

“…We examine the implicit healthy life expectancy (HLE) used for actuarial calculations in some selected biometric data sets from the US (Robinson 1996), Australia (Hariyanto et al 2014a, b) and China (Cui et al 2022). It is very difficult to find this health indicator explicitly presented in the actuarial literature on LTC, and even more difficult to find it for LCAs.…”

“…The total average rate ( d j 65 ) would be 49.47 and 65.15% for males and females respectively, which is far higher than the figures calculated in the case of Australia. Robinson (1996) Different levels of heterogeneity at the same level of dependence for males and females Big differences in the amount of time likely to be spent in a dependent state when compared to the official statistics and/or similar investigations Hariyanto et al (2014a, b) People in any state of core activity limitation can only improve by one category over a one-year interval Very high prevalence rates Cui et al (2022) Only two states of dependence Unhealthy life expectancy very high in comparison with other recent studies High recovery rates The mortality ratio presents sizeable irregularities for sections that are very difficult to understand and justify. We see inexplicable jumps for both males and females Lack of graduation in incidence and mortality rates Very high prevalence rates…”

“…Fig.5Comparison of mortality ratios: dependent/active people. Source: Own based on data fromCui et al (2022) …”