Prevention Incentive in Long Term Insurance Contracts with Considering Uncertainty in First Period

Long term insurance contracts such as health insurance and labour insurance face with moral hazard and adverse selection. In this article, we assume a two-period model that agent in the first period is young and he is old in the second period. In fact, the agent can decide on amount of effort in the first period in order to decrease his risk in the second period. We consider if there are moral hazard and probability of surviving of the agent in the first period, what effects they will have on classification risk and premium of the first and the second period. we will solvemodel with lagrangian method and we will find that under condition of moral hazard, if probability of surviving of the agent in the first period decreases, premium of first period and risk classification will increase. Also, we show that under these conditi ns, in the second period, the agent with high risk should pay more than the agent with low risk. We prove that the insurance company should determine the length of the first period that the agent survives with high probability.