Medical insurance after retirement: mathematical models

Abstract

Currently, Hong Kong residents enjoy one of the most generous public health care plans in the world. Most of the services are covered by public health insurance. Patients pay a small fraction of the costs for visits to doctors and hospital treatments. However, due to rising medical costs, declining government funding, and an aging population, the current public health plan will not be able to sustain, and more medical services will be covered by the private sector in the future. It is likely that additional medical insurance will be needed to cover the rising costs, especially for those who will retire in the future.===Based on this projection, the presenting company proposes a special medical insurance product, which covers the medical expenses of the clients only after retirement. The main question is, therefore, when an individual should start contribute toward this medical plan after retirement? In other words, if it is necessary to obtain such a plan, should an individual start the plan immediately, wait until he or she retires? If not, is there an optimal time to start contributing and how to determine the amount of the contribution?===We propose several mathematical models which may be used to answer these questions. We will restrict ourselves to an idealized situation by assuming that the premium charged by the insurance will be used only to cover the actual medical expenses. We will neglect other direct and indirect costs as well as the profit.