Doubly Enhanced Annuities (DEANs) and the Impact of Quality of Long-Term Care under a Multi-State Model of Activities of Daily Living (ADL)

The relatively small size of global voluntary immediate life annuity markets seemingly contradicts a well-known result that, under certain conditions, utility-maximizing retirees should annuitize all of their wealth upon retirement. This apparent contradiction contributes to what is called the “annuity puzzle.” The main explanations for the annuity puzzle include adverse selection, bequest motives, and retirees’ fear of health shocks that may require them to need long-term care. To explore a potential solution to this puzzle in the U.S. annuity market, we consider a cohort of retirees who are independent and identical except for a hidden immutable health parameter, θ>0, that identifies the retiree’s risk type. We assume that the “average” or “standard” retiree has θ = 1, with larger values of θ denoting less healthy individuals. Because private insurers fear that annuitants may live well beyond their life expectancy—that is, they fear adverse selection—voluntary immediate life annuities are generally priced in a manner that makes them attractive mainly to retirees who believe themselves to be healthier than average. These retirees, however, typically represent a small fraction of their cohort of retirees. To expand annuity markets, we are proposing a hybrid voluntary fixed immediate annuity product called a doubly enhanced annuity (DEAN), which we feel will be attractive to the larger retiree population; that is, retirees with θ>1. DEANs are medically underwritten to provide greater annual benefits to annuitants with shorter than average life expectancies, they provide long-term care benefits, and they satisfy a bequest motive through a death benefit. Our underlying model of retiree mortality and morbidity is based on a multi-state Markov process with states representing various levels of an insured retiree’s ability to perform activities of daily living (ADL). A major contribution of our research is to explicitly include in our multi-state Markov model a parameter, α, that reflects the level of quality of long-term care a retiree receives over her lifetime. Our main objectives are to develop a theoretical basis for pricing DEANs for the U.S. market, to determine a retiree’s expected discounted utility gained from these annuities, to determine the optimal choice of quality of care, and to explore some of the quality of life implications. A numerical example is provided.