Accounting for health shocks risk under annuity schemes

Existing literature documents the annuity puzzle, namely a low level of annuity purchase among retirees, at odds with the predictions of classical rational choice theory. In line with [1], one of the barriers to annuitization is the fear of health shocks, that, by reducing survival expectations, may in- duce people to deem not attractive a contract paying out benefits for a very long time horizon. Furthermore, individuals could be willing to keep a buffer against health expenses. A possible way to address these issues is that the annuity policy embeds the possibility to account for a severe disability incep- tion and, consequently, to adjust the annuity benefits signicantly, based on the updated survival expectations of the policyholder. In this respect, the literature proposes insurance products, such as the life care annuity([2, 3]). We investigate this type of contract, by adding features that may be relevant under both mathematical and insurance economics perspectives. For instance, to better match the policyholders' needs, we allow the option to withdraw a chosen amount or even to make a total lapse. This characterictic makes the product interesting from a mathematical point of view, as its evaluation requires solving a stochastic control problem. The traditional life care annuity product being a benchmark, we evaluate our proposed product through numerical algorithms. The main contribution consists in developing features of the annuity contracts potentially being able to overcome the barrier arising from the individuals' fear of health shocks, and in pricing such contracts through highly precise techniques being able to tackle the presence of non-standard surrender options.