To reach our research objectives we work according to the following steps.
1. Setting up a stochastic optimal control model with a random stopping rule, in which an individual decision-maker optimizes expected life-cycle utility over a consumption path and a path of health care. The latter is distinguished into preventive care, affecting the arrival rate of the shock, and curative care, affecting the survival process.
2. To develop a transformation to a vintage optimal control problem, which allows numerical tractability with established methods as well as deeper insights into the optimal behaviour.
3. To solve this model for the optimal life-cycle allocation and to develop from the mathematical first-order conditions economically intuitive behavioural rules as well as a value of survival/health, a value of prevention and a value of anticipation.
4. To calibrate the model to arrive at realistic life-cycle profiles of preventive and curative care and consumption and gain a quantitative understanding of the impact of large shocks to health and of the anticipation of such shocks.
· Different types of health shocks: i) onset of chronic disease, ii) one-off shock to health with perfect recovery, iii) debilitating shock to health
· Different types of insurances: i) annuities (no, full and partial annuitization), ii) health insurance, iii) disability insurance