This leads to the income payments in the MD state after 11 years being lower than the income payments in the D state since the balance in the MD state is lower than the balance in the D state and not enough to generate a higher income payment than the D state. [...] We can see that for the age 80 cohort, the income in the D state is higher than in the MD state because we observe that the probability of death in the D state is significantly higher than in the MD state after age 85, that is q3(t) > q4(t) for t > 5. [...] From the above illustration, we can see that the state-dependent accumulation factor depends on the initial state at the beginning of the year and also the state at the end of the year. [...] We can also see that the change in the H and M states are at a relatively low level at around 1%, while the change in the D state is around 4% ≠ 5% and the change in the MD state is around 13% ≠ 16%, indicating that with the proposed health state-dependent risk-sharing rule, the income in the less healthy state can be increased by a significant amount at a relatively small cost of the healthy memb. [...] We can also see from Figure 16 that for individuals aged 80 joined at time 0, the income payments in the D and MD states are 3 and 3.25 times the payments in the H state but last for a shorter period of time, which corresponds with the shorter life expectancy at age 80 in the D and MD states.
- Pages
- 40
- Published in
- Australia
Table of Contents
- Introduction 3
- Multi-state Health Model 5
- Multi-state Health-contingent Mortality Pooling 7
- Step 1: Health-contingent Accumulation 8
- Determining the State-dependent Accumulation Factors 10
- Step 2: Health-contingent Risk-sharing 11
- Step 3: Health-contingent Benefit Payments 13
- Step 4: Health-contingent Accumulation in the Next Period 14
- Summary of fund operation 14
- Numerical Illustration: Income Payments and Balances under Different Settings 15
- No Risk-Sharing, Pool Size=1 15
- Risk-sharing, Closed Pool, and No State-dependent Index 17
- Age=60, Pool Size=100 17
- Age=60, Pool Size=1000 19
- Risk-sharing, Open Pool and Mixed Cohort, and No State-dependent Accumulation Factor 19
- Risk-sharing, Open Pool, and State-dependent Accumulation Factors 22
- Numerical Illustration of Determining State-dependent Accumulation Factors 22
- Comparison of Incomes and Balances in Different Health States 23
- Confidence Intervals 25
- Multiple Transitions 27
- Level Payments: Risk-sharing, Open Pool, and State-dependent Accumulation Factors 28
- Multiple Transitions with Level Payments 31
- Conclusions 31
- Acknowledgements 32
- References 32
