The Impact of Health Impairment on Optimal Annuitization for Retirees

Post retirement, annuities provide a steady stream of income for retirees. However, the annuitization rate is relatively small in the insurance market in many countries around the world. Prior studies have shown that a substandard health status in retirement reduces annuitization due to adverse selection. Recent innovation introduces an enhanced annuity plan where individuals with impaired health are entitled to higher annuity payments. However, this market is less explored in countries other than the UK. This paper aims to study the optimal annuitization rate where both standard and substandard annuity rates are offered in the market. The life cycle model in this paper incorporates multiple health states based on the likelihood of events and quality of life measures. Our framework consists of two important parts. First, we estimate the transition probabilities of all health states in our Markov model using reliable national data. Second, we derive the optimal consumption and annuitization solution to maximize a retiree's expected lifetime utility given the uncertainty of future health risk. In addition, we also consider the bequest motive in our optimization problem. Our results show that the optimal annuitization is driven by the choice of bequest and risk-aversion parameters, as well as the health status of the annuitant. Whilst the health-dependent utility parameter only affects our results for certain cases.