Analysis of fair fee in guaranteed lifelong withdrawal and Markovian health benefits

This study proposed and evaluated a new insurance product, i.e., the variable annuity product, accompanied by the health status and the guaranteed lifelong withdrawal benefit (GLWB). Due to specific problems, the insurance sector is now one of the riskiest industries. The aging of the population and rising medical service costs as a result of technological advancements are to blame for this. Thus one of the most basic needs in the health insurance sector is to design an innovative product. In this article, a mixed discrete-continuous time model is proposed to calculate the fair fee of the product, calculated using equilibrium condition between premium and benefits. We considered constant volatility and rate of interest along with health status benefits and hospitalization coverage. For an illustration of the capability of this product and some possible improvements in the product, a numerical study, and sensitivity analysis have been conducted. The results showed that the withdrawal amount and age have a significant impact on the cost. A rise in the initial insured age and withdrawal amount increases the fair fee of the product. The GLWB rider’s guaranteed amount and medical expenses are included in the withdrawal amount.