In recent years, a number of health insurers have introduced a reward gain type of wellness programs that can reduce the medical costs by encouraging the behavior change of health insurance subscribers to improve health. In the programs, insurers have to determine a reward strategy in order to strive the insurance subscribers. In this paper, we study the insurer's incentive designing problem of wellness programs. We formulate the insurer's incentive designing problem as a dynamic principal-agent problem. We derive the sufficient conditions for the existences of the optimal reward strategy, the optimal health-support service strategy, and the incentive compatible effort recommended to the insurance subscribers. We also discuss the effects of the insurer's risk-sensitivity on the optimal strategies. We use a numerical example to show the computation aspects of the problem.
In this paper, we propose a simple method for performing a comparative statics analysis of the expectation of the first passage times to the optimal thresholds in the real options model. Also, we show that this method is suitable for a comparative statics analysis of the variance of the first passage times. Furthermore, this method can help us for understanding the results of the comparative statics analysis.